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Seminar information archive
Seminar information archive ～04/18｜Today's seminar 04/19 | Future seminars 04/20～
thesis presentations
15:45-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Kenichi KONDO (Guraduate School of Mathematical Sciences the University of Tokyo)
Symmetrized Max-Plus Algebra and Ultradiscrete sine-Gordon Equation (JAPANESE)
Kenichi KONDO (Guraduate School of Mathematical Sciences the University of Tokyo)
Symmetrized Max-Plus Algebra and Ultradiscrete sine-Gordon Equation (JAPANESE)
thesis presentations
09:45-11:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Tomoyuki HISAMOTO (Guraduate School of Mathematical Sciences the University of Tokyo)
Asymptotic analysis of Bergman kernels for linear series and its application to Kahler Geometry (JAPANESE)
Tomoyuki HISAMOTO (Guraduate School of Mathematical Sciences the University of Tokyo)
Asymptotic analysis of Bergman kernels for linear series and its application to Kahler Geometry (JAPANESE)
thesis presentations
11:00-12:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshihiko MATSUMOTO (Guraduate School of Mathematical Sciences the University of Tokyo)
Asymptotically complex hyperbolic Einstein metrics and CR geometry (JAPANESE)
Yoshihiko MATSUMOTO (Guraduate School of Mathematical Sciences the University of Tokyo)
Asymptotically complex hyperbolic Einstein metrics and CR geometry (JAPANESE)
thesis presentations
13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Tomoro ASAI (Guraduate School of Mathematical Sciences the University of Tokyo)
Analytic semigroup approach to higher order quasilinear parabolic problems (JAPANESE)
Tomoro ASAI (Guraduate School of Mathematical Sciences the University of Tokyo)
Analytic semigroup approach to higher order quasilinear parabolic problems (JAPANESE)
thesis presentations
14:15-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Makoto MIURA (Guraduate School of Mathematical Sciences the University of Tokyo)
Hibi toric varieties and mirror symmetry (JAPANESE)
Makoto MIURA (Guraduate School of Mathematical Sciences the University of Tokyo)
Hibi toric varieties and mirror symmetry (JAPANESE)
thesis presentations
15:45-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Tomohiko ISHIDA (Guraduate School of Mathematical Sciences the University of Tokyo)
Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk (JAPANESE)
Tomohiko ISHIDA (Guraduate School of Mathematical Sciences the University of Tokyo)
Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk (JAPANESE)
GCOE Seminars
17:00-18:30 Room #370 (Graduate School of Math. Sci. Bldg.)
Asaf Iskandarov (Lenkaran State University)
Identification of quantum potentials in the Schrodinger equation (ENGLISH)
Asaf Iskandarov (Lenkaran State University)
Identification of quantum potentials in the Schrodinger equation (ENGLISH)
[ Abstract ]
In this lecture I will consider the identification problem of determining the unknown time-dependent coefficients of nonlinear Schrodinger equation.We applied the variational method and studied the correctness of direct and identification problems. We find a necessary condition of the solution and give a stable methed for solution.
In this lecture I will consider the identification problem of determining the unknown time-dependent coefficients of nonlinear Schrodinger equation.We applied the variational method and studied the correctness of direct and identification problems. We find a necessary condition of the solution and give a stable methed for solution.
Seminar on Probability and Statistics
11:00-12:10 Room #006 (Graduate School of Math. Sci. Bldg.)
Stefano M. Iacus (Dipartimento di Economia, Managemente Metodi Quantitativi Universita' di Milano)
On L^p model selection for discretely observed diffusion processes (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/14.html
Stefano M. Iacus (Dipartimento di Economia, Managemente Metodi Quantitativi Universita' di Milano)
On L^p model selection for discretely observed diffusion processes (JAPANESE)
[ Abstract ]
The LASSO is a widely used L^2 statistical methodology for simultaneous estimation and variable selection. In the last years, many authors analyzed this technique from a theoretical and applied point of view. In the first part of the seminar, we introduce and study the adaptive LASSO problem for discretely observed ergodic diffusion processes We prove oracle properties also deriving the asymptotic distribution of the LASSO estimator. In the second part of the seminar we present general L^p approach for stochastic differential equations with small diffusion noise. Finally, we present simulated and real data analysis to provide some evidence on the applicability of this method.
FMSP Lectures
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
[ Reference URL ]The LASSO is a widely used L^2 statistical methodology for simultaneous estimation and variable selection. In the last years, many authors analyzed this technique from a theoretical and applied point of view. In the first part of the seminar, we introduce and study the adaptive LASSO problem for discretely observed ergodic diffusion processes We prove oracle properties also deriving the asymptotic distribution of the LASSO estimator. In the second part of the seminar we present general L^p approach for stochastic differential equations with small diffusion noise. Finally, we present simulated and real data analysis to provide some evidence on the applicability of this method.
FMSP Lectures
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/14.html
2013/02/05
Lie Groups and Representation Theory
17:30-19:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Nizar Demni (Université de Rennes 1)
Dunkl processes assciated with dihedral systems, II (ENGLISH)
Nizar Demni (Université de Rennes 1)
Dunkl processes assciated with dihedral systems, II (ENGLISH)
[ Abstract ]
I'll focus on dihedral systems and its semi group density. I'll show how one can write down this density using probabilistic techniques and give some interpretation using spherical harmonics. I'll also present some results attempting to get a close formula for the density: the main difficulty comes then from the inversion (in composition sense) of Tchebycheff polynomials of the first kind in some neighborhood. Finally, I'll display expressions through known special functions for even dihedral groups, and the unexplained connection between the obtained formulas and those of Ben Said-Kobayashi-Orsted.
I'll focus on dihedral systems and its semi group density. I'll show how one can write down this density using probabilistic techniques and give some interpretation using spherical harmonics. I'll also present some results attempting to get a close formula for the density: the main difficulty comes then from the inversion (in composition sense) of Tchebycheff polynomials of the first kind in some neighborhood. Finally, I'll display expressions through known special functions for even dihedral groups, and the unexplained connection between the obtained formulas and those of Ben Said-Kobayashi-Orsted.
2013/02/04
Lie Groups and Representation Theory
17:30-19:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Nizar Demni (Université de Rennes 1)
Dunkl processes assciated with dihedral systems, I (ENGLISH)
Nizar Demni (Université de Rennes 1)
Dunkl processes assciated with dihedral systems, I (ENGLISH)
[ Abstract ]
I'll first give a brief and needed account on root systems and finite reflection groups. Then, I'll introduce Dunkl operators and give some properties. Once I'll do, I'll introduce Dunkl processes and their continuous components, so-called radial Dunkl processes. The latter generalize eigenvalues processes of some matrix-valued processes and reduces to reflected Brownian motion in Weyl chambers. Besides, Brownian motion in Weyl chambers corresponds to all multiplicity values equal one are constructed from a Brownian motion killed when it first hits the boundary of the Weyl chamber using the unique positive harmonic function (up to a constant) on the Weyl chamber. In the analytic side, determinantal formulas appear and are related to harmonic analysis on the Gelfand pair (Gl(n,C), U(n)). This is in agreement on the one side with the so-called reflection principle in stochastic processes theory and matches on the other side the so-called shift principle introduced by E. Opdam. Finally, I'll discuss the spectacular result of Biane-Bougerol-O'connell yielding to a Duistermaat-Heckman distribution for non crystallographic systems.
I'll first give a brief and needed account on root systems and finite reflection groups. Then, I'll introduce Dunkl operators and give some properties. Once I'll do, I'll introduce Dunkl processes and their continuous components, so-called radial Dunkl processes. The latter generalize eigenvalues processes of some matrix-valued processes and reduces to reflected Brownian motion in Weyl chambers. Besides, Brownian motion in Weyl chambers corresponds to all multiplicity values equal one are constructed from a Brownian motion killed when it first hits the boundary of the Weyl chamber using the unique positive harmonic function (up to a constant) on the Weyl chamber. In the analytic side, determinantal formulas appear and are related to harmonic analysis on the Gelfand pair (Gl(n,C), U(n)). This is in agreement on the one side with the so-called reflection principle in stochastic processes theory and matches on the other side the so-called shift principle introduced by E. Opdam. Finally, I'll discuss the spectacular result of Biane-Bougerol-O'connell yielding to a Duistermaat-Heckman distribution for non crystallographic systems.
2013/01/30
Geometry Colloquium
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ryoichi Kobayashi (Nagoya University)
Hamiltonian Volume Minimizing Property of Maximal Torus Orbits in the Complex Projective Space (JAPANESE)
Ryoichi Kobayashi (Nagoya University)
Hamiltonian Volume Minimizing Property of Maximal Torus Orbits in the Complex Projective Space (JAPANESE)
[ Abstract ]
We prove that any $U(1)^n$-orbit in $\\Bbb P^n$ is volume minimizing under Hamiltonian deformation.
The idea of the proof is :
- (1) We extend one $U(1)^n$-orbit to the momentum torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and consider its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$ where $\\phi$ is a Hamiltobian diffeomorphism of $\\Bbb P^n$,
and then :
- (2) We compare each $U(1)^n$-orbit and its Hamiltonian deformation by compaing the large $k$ asymptotic behavior of the sequence of projective embeddings defined, for each $k$, by the basis of $H^0(\\Bbb P^n,\\Cal O(k))$ obtained by semi-classical approximation of the $\\Cal O(k)$ Bohr-Sommerfeld tori of the Lagrangian torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$.
We prove that any $U(1)^n$-orbit in $\\Bbb P^n$ is volume minimizing under Hamiltonian deformation.
The idea of the proof is :
- (1) We extend one $U(1)^n$-orbit to the momentum torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and consider its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$ where $\\phi$ is a Hamiltobian diffeomorphism of $\\Bbb P^n$,
and then :
- (2) We compare each $U(1)^n$-orbit and its Hamiltonian deformation by compaing the large $k$ asymptotic behavior of the sequence of projective embeddings defined, for each $k$, by the basis of $H^0(\\Bbb P^n,\\Cal O(k))$ obtained by semi-classical approximation of the $\\Cal O(k)$ Bohr-Sommerfeld tori of the Lagrangian torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$.
Lectures
17:30-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Antonio Degasperis (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
Antonio Degasperis (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
[ Abstract ]
A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.
A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.
Lectures
17:30-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Antonio Degasperis (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
Antonio Degasperis (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
[ Abstract ]
A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.
A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.
Lectures
17:30-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Antonio Degasperis (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
Antonio Degasperis (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
[ Abstract ]
A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.
A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.
Lectures
09:45-10:45 Room #123 (Graduate School of Math. Sci. Bldg.)
Marzieh Forough (Ferdowsi Univ. Mashhad)
Stability of Fredholm property of regular operators on Hilbert $C^*$-modules (ENGLISH)
Marzieh Forough (Ferdowsi Univ. Mashhad)
Stability of Fredholm property of regular operators on Hilbert $C^*$-modules (ENGLISH)
Lectures
11:00-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Gerardo Morsella (Univ. Roma II)
Scaling algebras, superselection theory and asymptotic morphisms (ENGLISH)
Gerardo Morsella (Univ. Roma II)
Scaling algebras, superselection theory and asymptotic morphisms (ENGLISH)
Lectures
13:30-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Joav Orovitz (Ben-Gurion Univ.)
Tracially $\\mathcal{Z}$-absorbing $C^*$-algebras (ENGLISH)
Joav Orovitz (Ben-Gurion Univ.)
Tracially $\\mathcal{Z}$-absorbing $C^*$-algebras (ENGLISH)
Lectures
14:45-15:45 Room #118 (Graduate School of Math. Sci. Bldg.)
Nicola Watson (Univ. Toronto)
Noncommutative covering dimension (ENGLISH)
Nicola Watson (Univ. Toronto)
Noncommutative covering dimension (ENGLISH)
Lectures
16:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Marcel Bischoff (Univ. G\"ottingen)
Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)
Marcel Bischoff (Univ. G\"ottingen)
Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)
Lectures
17:15-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Hiroki Asano (Univ. Tokyo)
Group actions with Rohlin property (ENGLISH)
Hiroki Asano (Univ. Tokyo)
Group actions with Rohlin property (ENGLISH)
GCOE Seminars
16:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Marcel Bischoff (Univ. Göttingen)
Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-3.htm
Marcel Bischoff (Univ. Göttingen)
Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-3.htm
2013/01/28
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Taiji MARUGAME (MS U-Tokyo)
Renormalized Chern-Gauss-Bonnet formula for complete Kaehler-Einstein metrics (JAPANESE)
Taiji MARUGAME (MS U-Tokyo)
Renormalized Chern-Gauss-Bonnet formula for complete Kaehler-Einstein metrics (JAPANESE)
Seminar on Probability and Statistics
13:00-14:10 Room #006 (Graduate School of Math. Sci. Bldg.)
Ernst August Frhr. v. Hammerstein (Albert-Ludwigs-Universität Freiburg)
Laplace and Fourier based valuation methods in exponential Levy models (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/13.html
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
Ernst August Frhr. v. Hammerstein (Albert-Ludwigs-Universität Freiburg)
Laplace and Fourier based valuation methods in exponential Levy models (JAPANESE)
[ Abstract ]
A fundamental problem in mathematical finance is the explicit computation of expectations which arise as prices of derivatives. Closed formulas that can easily be evaluated are typically only available in models driven by a Brownian motion. If one considers more sophisticated jump-type Levy processes as drivers, the problem quickly becomes rather nontrivial and complicated. Starting with the paper of Carr and Madan (1999) and the PhD thesis of Raible (2000), Laplace and Fourier based methods have been used to derive option pricing formulas that can be evaluated very efficiently numerically. In this talk we review the initial idea of Raible (2000), show how it can be generalized and discuss under which precise mathematical assumptions the Laplace and Fourier approach work. We then give several examples of specific options and Levy models to which the general framework can be applied to. In the last part, we present some formulas for pricing options on the supremum and infimum of the asset price process that use the Wiener-Hopf factorization.
FMSP Lectures
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
[ Reference URL ]A fundamental problem in mathematical finance is the explicit computation of expectations which arise as prices of derivatives. Closed formulas that can easily be evaluated are typically only available in models driven by a Brownian motion. If one considers more sophisticated jump-type Levy processes as drivers, the problem quickly becomes rather nontrivial and complicated. Starting with the paper of Carr and Madan (1999) and the PhD thesis of Raible (2000), Laplace and Fourier based methods have been used to derive option pricing formulas that can be evaluated very efficiently numerically. In this talk we review the initial idea of Raible (2000), show how it can be generalized and discuss under which precise mathematical assumptions the Laplace and Fourier approach work. We then give several examples of specific options and Levy models to which the general framework can be applied to. In the last part, we present some formulas for pricing options on the supremum and infimum of the asset price process that use the Wiener-Hopf factorization.
FMSP Lectures
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/13.html
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
GCOE Seminars
16:00-17:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Bernadette Miara (Universite Paris-Est)
The obstacle problem for a shallow membrane-Justification and stability (ENGLISH)
Bernadette Miara (Universite Paris-Est)
The obstacle problem for a shallow membrane-Justification and stability (ENGLISH)
[ Abstract ]
This lecture is twofold.
In the first part we recall the difference between the three-dimensional unilateral contact problem (the so-called Signorini problem) and its two-dimensional limit (the obstacle problem) in the case of an elastic shell as it was considered in [1] and [2].
In the second part we consider a simplified set of equations which describe the equilibrium equations of a shallow membrane (as justified in [3]) in contact with a plane obstacle and we study the stability of the contact zone with respect to small changes of the applied force, which amounts to studying the variation of the boundary of this contact zone. This kind of stability was first established in the scalar case for the Laplacian operator [4] then for the biharmonic operator [5]. The interest of the vectorial case considered here is due to the coupling effects between the in-plane and the transverse components of the displacement field in the framework of linearized Marguerre-von K´arm´an shell model.
This is a joint work with Alain L´eger, CNRS, Laboratoire de M´ecanique et d’Acoustique, 13402, Marseille, France.
This lecture is twofold.
In the first part we recall the difference between the three-dimensional unilateral contact problem (the so-called Signorini problem) and its two-dimensional limit (the obstacle problem) in the case of an elastic shell as it was considered in [1] and [2].
In the second part we consider a simplified set of equations which describe the equilibrium equations of a shallow membrane (as justified in [3]) in contact with a plane obstacle and we study the stability of the contact zone with respect to small changes of the applied force, which amounts to studying the variation of the boundary of this contact zone. This kind of stability was first established in the scalar case for the Laplacian operator [4] then for the biharmonic operator [5]. The interest of the vectorial case considered here is due to the coupling effects between the in-plane and the transverse components of the displacement field in the framework of linearized Marguerre-von K´arm´an shell model.
This is a joint work with Alain L´eger, CNRS, Laboratoire de M´ecanique et d’Acoustique, 13402, Marseille, France.
2013/01/26
Harmonic Analysis Komaba Seminar
13:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Guorong, Hu
(Tokyo Univesity) 13:30-15:00
On Triebel-Lizorkin spaces on Stratified Lie groups
(ENGLISH)
Profiles of solutions to an integral system related to
the weighted Hardy-Littlewood-Sobolev inequality
(JAPANESE)
Guorong, Hu
(Tokyo Univesity) 13:30-15:00
On Triebel-Lizorkin spaces on Stratified Lie groups
(ENGLISH)
[ Abstract ]
We introduce the notion of Triebel-Lizorkin spaces
$\\dot{F}^{s}_{p,q}(G)$ on a stratified Lie group $G$
in terms of a Littlewood-Paley-type decomposition
with respect to a sub-Laplacian $\\mathscr{L}$ of $G$,
for $s \\in \\mathbb{R}$, $0We show that the scale of these spaces is actually independent of
the precise choice of the sub-Laplacian
and the Littlewood-Paley-type decomposition.
As we shall see, many properties of the classical
Triebel-Lizorkin spaces on $\\mathbb{R}^{n}$, e.g.,
lifting property, embeddings and dual property,
can be extended to the setting of stratified Lie groups
without too much effort.
We then study the boundedness of convolution operators
on these spaces and finally,
we obtain a Hormander type spectral multipliers theorem.
Michiaki, Onodera (Kyushu University) 15:30-17:00We introduce the notion of Triebel-Lizorkin spaces
$\\dot{F}^{s}_{p,q}(G)$ on a stratified Lie group $G$
in terms of a Littlewood-Paley-type decomposition
with respect to a sub-Laplacian $\\mathscr{L}$ of $G$,
for $s \\in \\mathbb{R}$, $0We show that the scale of these spaces is actually independent of
the precise choice of the sub-Laplacian
and the Littlewood-Paley-type decomposition.
As we shall see, many properties of the classical
Triebel-Lizorkin spaces on $\\mathbb{R}^{n}$, e.g.,
lifting property, embeddings and dual property,
can be extended to the setting of stratified Lie groups
without too much effort.
We then study the boundedness of convolution operators
on these spaces and finally,
we obtain a Hormander type spectral multipliers theorem.
Profiles of solutions to an integral system related to
the weighted Hardy-Littlewood-Sobolev inequality
(JAPANESE)
[ Abstract ]
We study the Euler-Lagrange system for a variational problem
associated with the weighted Hardy-Littlewood-Sobolev inequality of
Stein and Weiss.
We show that all the nonnegative solutions to the system are radially
symmetric and have particular profiles around the origin and the
infinity.
This work extends previous results obtained by other authors to the
general case.
We study the Euler-Lagrange system for a variational problem
associated with the weighted Hardy-Littlewood-Sobolev inequality of
Stein and Weiss.
We show that all the nonnegative solutions to the system are radially
symmetric and have particular profiles around the origin and the
infinity.
This work extends previous results obtained by other authors to the
general case.
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