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Tuesday Seminar of Analysis
Seminar information archive ～09/18｜Next seminar｜Future seminars 09/19～
| Date, time & place | Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi |
Seminar information archive
2010/09/28
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Pavel Exner (Czech Academy of Sciences)
Some spectral and resonance properties of quantum graphs (ENGLISH)
Pavel Exner (Czech Academy of Sciences)
Some spectral and resonance properties of quantum graphs (ENGLISH)
[ Abstract ]
In this talk I will discuss three new results about Schr¨odinger operators
on metric graphs obtained in collaboration with Jiri Lipovskyand Brian Davies.
The first one is related to invalidity of the uniform continuation principle for such
operators. One manifestation of this fact are embedded eigenvalues due to
rational relations of graph edge lengths. This effect is non-generic and we show
how geometric perturbations turn these embedded eigenvalues into resonances.
Then second problem is related to high-energy behavior of resonances: we extend
a recent result of Davies and Pushnitski to graphs with general vertex couplings
and find conditions under which the asymptotics does not have Weyl character.
Finally, the last question addressed here concerns the absolutely continuous spectrum
of radial-tree graphs. In a similar vein, we generalize a recent result by Breuer and
Frank that in case of the free (or Kirhhoff) coupling the ac spectrum is absent
provided the edge length are increasing without a bound along the tree.
We show that the result remains valid for a large class of vertex couplings,
but on the other hand, there are nontrivial couplings leading to an ac spectrum.
In this talk I will discuss three new results about Schr¨odinger operators
on metric graphs obtained in collaboration with Jiri Lipovskyand Brian Davies.
The first one is related to invalidity of the uniform continuation principle for such
operators. One manifestation of this fact are embedded eigenvalues due to
rational relations of graph edge lengths. This effect is non-generic and we show
how geometric perturbations turn these embedded eigenvalues into resonances.
Then second problem is related to high-energy behavior of resonances: we extend
a recent result of Davies and Pushnitski to graphs with general vertex couplings
and find conditions under which the asymptotics does not have Weyl character.
Finally, the last question addressed here concerns the absolutely continuous spectrum
of radial-tree graphs. In a similar vein, we generalize a recent result by Breuer and
Frank that in case of the free (or Kirhhoff) coupling the ac spectrum is absent
provided the edge length are increasing without a bound along the tree.
We show that the result remains valid for a large class of vertex couplings,
but on the other hand, there are nontrivial couplings leading to an ac spectrum.
2010/07/13
17:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Carlos Villegas Blas (Universidad Nacional Autonoma de Mexico)
On a limiting eigenvalue distribution theorem for perturbations of the hydrogen atom (JAPANESE)
Carlos Villegas Blas (Universidad Nacional Autonoma de Mexico)
On a limiting eigenvalue distribution theorem for perturbations of the hydrogen atom (JAPANESE)
[ Abstract ]
Let H be the hydrogen atom Hamiltonian. We will show that
the operator H+P can have well defined clusters of eigenvalues
for a suitable perturbation P=f(h)Q where Q is a pseudo-differential
operator of order zero and f(h) is a small quantity depending of
the Planck's parameter h. We will show that the distribution of
eigenvalues in those clusters has a semi-classical limit involving
the averages of the principal symbol of Q along the classical orbits
of the Kepler problem.
Let H be the hydrogen atom Hamiltonian. We will show that
the operator H+P can have well defined clusters of eigenvalues
for a suitable perturbation P=f(h)Q where Q is a pseudo-differential
operator of order zero and f(h) is a small quantity depending of
the Planck's parameter h. We will show that the distribution of
eigenvalues in those clusters has a semi-classical limit involving
the averages of the principal symbol of Q along the classical orbits
of the Kepler problem.
2010/06/22
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ivana Alexandrova (East Carolina University)
Resonances for Magnetic Scattering by Two Solenoidal Fields at Large Separation (ENGLISH)
Ivana Alexandrova (East Carolina University)
Resonances for Magnetic Scattering by Two Solenoidal Fields at Large Separation (ENGLISH)
[ Abstract ]
We consider the problem of quantum resonances in magnetic scattering by two
solenoidal fields at large separation in two dimensions, and we study how a trajectory
oscillating between the two fields gives rise to resonances near the real axis when
the distance between two centers of fields goes to infinity. We give a sharp lower
bound on resonance widths in terms of backward amplitudes calculated explicitly for
scattering by each solenoidal field. The study is based on a new type of complex
scaling method. As an application, we also discuss the relation to semiclassical
resonances in scattering by two solenoidal fields. This is joint work with Hideo Tamura.
We consider the problem of quantum resonances in magnetic scattering by two
solenoidal fields at large separation in two dimensions, and we study how a trajectory
oscillating between the two fields gives rise to resonances near the real axis when
the distance between two centers of fields goes to infinity. We give a sharp lower
bound on resonance widths in terms of backward amplitudes calculated explicitly for
scattering by each solenoidal field. The study is based on a new type of complex
scaling method. As an application, we also discuss the relation to semiclassical
resonances in scattering by two solenoidal fields. This is joint work with Hideo Tamura.
2010/06/15
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takashi Takiguchi (Department of Mathematics, National Defense Academy)
Sato's counterexample and the structure of generalized functions (JAPANESE)
Takashi Takiguchi (Department of Mathematics, National Defense Academy)
Sato's counterexample and the structure of generalized functions (JAPANESE)
[ Abstract ]
In this talk, we discuss the relation between the structure and the microlocal unique continuation property of generalized functions. We also mention some applications of the microlocal unique continuation property.
In this talk, we discuss the relation between the structure and the microlocal unique continuation property of generalized functions. We also mention some applications of the microlocal unique continuation property.
2010/04/13
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Jean-Marc Bouclet (Toulouse University, France)
Strichartz estimates and the Isozaki-Kitada parametrix
on asymptotically hyperbolic manifolds (ENGLISH)
Jean-Marc Bouclet (Toulouse University, France)
Strichartz estimates and the Isozaki-Kitada parametrix
on asymptotically hyperbolic manifolds (ENGLISH)
2010/01/26
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Jacob S. Christiansen (コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)
Jacob S. Christiansen (コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)
2010/01/19
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
岡田 靖則 (千葉大・理)
超函数の有界性と Massera 型定理について
岡田 靖則 (千葉大・理)
超函数の有界性と Massera 型定理について
2009/11/24
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
吉野 邦生 (東京都市大学)
Analytic Properties of Eigen Values of Daubechies Localization Operator
吉野 邦生 (東京都市大学)
Analytic Properties of Eigen Values of Daubechies Localization Operator
[ Abstract ]
1)ドーベシー局在化作用素の固有値の解析的性質、積分表示式、
(2)ドーベシー局在化作用素のシンボルの再現公式、
(3)ドーベシー局在化作用素のバーグマンーフォック空間での表示
等について述べる。
1)ドーベシー局在化作用素の固有値の解析的性質、積分表示式、
(2)ドーベシー局在化作用素のシンボルの再現公式、
(3)ドーベシー局在化作用素のバーグマンーフォック空間での表示
等について述べる。
2009/09/15
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
打越 敬祐 (防衛大学校数学教育室)
渦層の超局所解析
打越 敬祐 (防衛大学校数学教育室)
渦層の超局所解析
[ Abstract ]
渦層とは,2次元流体が界面を境に2層に分かれて流れる状態で,今井功氏は「佐藤超関数は渦層である」と言っている.この考え方を用いると,
界面の時間変化を記述するBirkoff-Rott方程式を,擬微分方程式に書き直して解けることを説明する.
渦層とは,2次元流体が界面を境に2層に分かれて流れる状態で,今井功氏は「佐藤超関数は渦層である」と言っている.この考え方を用いると,
界面の時間変化を記述するBirkoff-Rott方程式を,擬微分方程式に書き直して解けることを説明する.
2009/07/21
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Georgi Raikov (PUC, Chile)
Low Energy Asymptotics of the SSF for Pauli Operators with Non-Constant Magnetic Fields
Georgi Raikov (PUC, Chile)
Low Energy Asymptotics of the SSF for Pauli Operators with Non-Constant Magnetic Fields
[ Abstract ]
In my talk, I will consider the 3D Pauli operator with non-constant magnetic field of constant direction,
perturbed by a matrix-valued electric potential which decays fast enough at infinity. I will discuss
the low-energy asymptotics of the associated spectral shift function which is proportional to the eigenvalue
counting function at negative energies, and to the scattering phase at positive energies.
In my talk, I will consider the 3D Pauli operator with non-constant magnetic field of constant direction,
perturbed by a matrix-valued electric potential which decays fast enough at infinity. I will discuss
the low-energy asymptotics of the associated spectral shift function which is proportional to the eigenvalue
counting function at negative energies, and to the scattering phase at positive energies.
2009/06/30
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ivana Alexandrova (東京大数理)
The Structure of the Scattering Amplitude for Schrodinger Operators with a Strong Magnetic Field
Ivana Alexandrova (東京大数理)
The Structure of the Scattering Amplitude for Schrodinger Operators with a Strong Magnetic Field
[ Abstract ]
We study the microlocal structure of the semi-classical scattering amplitude for Schrodinger operators with a strong magnetic field at non-trapping energies. We prove that, up to any order, the scattering amplitude can be approximated by a semi-classical pseudodifferential-operator-valued Fourier integral operator.
We study the microlocal structure of the semi-classical scattering amplitude for Schrodinger operators with a strong magnetic field at non-trapping energies. We prove that, up to any order, the scattering amplitude can be approximated by a semi-classical pseudodifferential-operator-valued Fourier integral operator.
2009/06/02
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
神本 晋吾 (東京大数理)
無限階擬微分作用素の形式核関数について
神本 晋吾 (東京大数理)
無限階擬微分作用素の形式核関数について
2009/05/26
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Myriam Ounaies (Strasbourg大学数学科)
Intrepolation problems in H￥"ormander algebras
Myriam Ounaies (Strasbourg大学数学科)
Intrepolation problems in H￥"ormander algebras
[ Abstract ]
We call Hörmander algebras the spaces $A_p(\\mathbb C)$ of entire functions $f$ such that, for all $z$ in $\\mathbb C$, \\[|f(z)|\\le Ae^{Bp(z)},\\] where $A$ and $B$ are some positive constants (depending on $f$) and $p$ is a subharmonic weight. We consider the following interpolation problem : Given a discrete sequence $\\{a_j\\}$ of complex numbers and a sequence of complex values $\\{b_j\\}$, under what conditions does there exist a function $f\\in A_p(\\mathbb C)$ such that $f(a_j)=b_j$ for all $j$ ? In other words, what is the trace of $A_p(\\mathbb C)$ on $\\{a_j\\}$ ?
We say that $\\{a_j\\}$ is an interpolating sequence if the trace is defined by the space of all $\\{b_j\\}$ satisfying $|b_j|\\le A'e^{B'p(a_j)}$, for some constants $A',B'>0$.
We use Hörmander's $L^2$-estimates for the $\\bar\\partial$-equation to describe the trace when the weight $p$ is radial and doubling and to characterize the interpolating sequences for more general weights.
We call Hörmander algebras the spaces $A_p(\\mathbb C)$ of entire functions $f$ such that, for all $z$ in $\\mathbb C$, \\[|f(z)|\\le Ae^{Bp(z)},\\] where $A$ and $B$ are some positive constants (depending on $f$) and $p$ is a subharmonic weight. We consider the following interpolation problem : Given a discrete sequence $\\{a_j\\}$ of complex numbers and a sequence of complex values $\\{b_j\\}$, under what conditions does there exist a function $f\\in A_p(\\mathbb C)$ such that $f(a_j)=b_j$ for all $j$ ? In other words, what is the trace of $A_p(\\mathbb C)$ on $\\{a_j\\}$ ?
We say that $\\{a_j\\}$ is an interpolating sequence if the trace is defined by the space of all $\\{b_j\\}$ satisfying $|b_j|\\le A'e^{B'p(a_j)}$, for some constants $A',B'>0$.
We use Hörmander's $L^2$-estimates for the $\\bar\\partial$-equation to describe the trace when the weight $p$ is radial and doubling and to characterize the interpolating sequences for more general weights.
2009/04/28
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
下村 明洋 (首都大学東京)
非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動(北直泰氏との共同研究)
下村 明洋 (首都大学東京)
非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動(北直泰氏との共同研究)
2009/01/20
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
吉野 邦生 (武蔵工業大学)
Generating function of eigenvalues of Daubechies Localization Operator
吉野 邦生 (武蔵工業大学)
Generating function of eigenvalues of Daubechies Localization Operator
[ Abstract ]
Daubechies Localization Operator の 固有値の母関数から symbol 関数を再現する公式について
Daubechies Localization Operator の 固有値の母関数から symbol 関数を再現する公式について
2009/01/12
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Jacob S. Christiansen
(コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)
Jacob S. Christiansen
(コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)
2008/11/25
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ovidiu Calin (Eastern Michigan University)
Heat kernels for subelliptic operators
Ovidiu Calin (Eastern Michigan University)
Heat kernels for subelliptic operators
[ Abstract ]
Subelliptic operators are differential operators with missing
directions. Their behavior is very different than the behavior or
elliptic operators. Among the most well known subelliptic operators
are the Grusin operator, the Heisenberg operator, and the Kolmogorov
operator. There are several methods of finding the heat kernels of
subelliptic operators. The heat kernels of subelliptic operators are
usually represented in integral form, but in the case of the
Kolmogorov operator we shall show that the heat kernel is of function
type. We shall spend some time on other subelliptic operators too.
Subelliptic operators are differential operators with missing
directions. Their behavior is very different than the behavior or
elliptic operators. Among the most well known subelliptic operators
are the Grusin operator, the Heisenberg operator, and the Kolmogorov
operator. There are several methods of finding the heat kernels of
subelliptic operators. The heat kernels of subelliptic operators are
usually represented in integral form, but in the case of the
Kolmogorov operator we shall show that the heat kernel is of function
type. We shall spend some time on other subelliptic operators too.
2008/11/11
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
新國 裕昭 (首都大学東京)
Rotation number approach to spectral analysis of the generalized Kronig-Penney Hamiltonians
新國 裕昭 (首都大学東京)
Rotation number approach to spectral analysis of the generalized Kronig-Penney Hamiltonians
2008/10/28
17:00-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Serge Alinhac (パリ大学オルセイ校)
Introduction to geometric analysis of hyperbolic equations
Serge Alinhac (パリ大学オルセイ校)
Introduction to geometric analysis of hyperbolic equations
2008/10/14
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
George Sell (ミネソタ大学)
Thin 3D Navier-Stokes equations: Ultimate boundedness of solutions with large data and global attractors
George Sell (ミネソタ大学)
Thin 3D Navier-Stokes equations: Ultimate boundedness of solutions with large data and global attractors
[ Abstract ]
グローバルCOE連続講演会と共催です.詳細はそちらをご覧ください.
グローバルCOE連続講演会と共催です.詳細はそちらをご覧ください.
2008/05/20
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Vania Sordoni (ボローニャ大学)
Wave operators for diatomic molecules
Vania Sordoni (ボローニャ大学)
Wave operators for diatomic molecules
2008/05/13
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Andr\'e Martinez (ボローニャ大学)
Resonances for non-analytic potentials (joint work with T. Ramond and J. Sj\\"ostrand)
Andr\'e Martinez (ボローニャ大学)
Resonances for non-analytic potentials (joint work with T. Ramond and J. Sj\\"ostrand)
2008/03/13
15:00-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
伊藤健一 (東京大学大学院数理科学研究科) 15:00-16:00
Schr/"odinger equations on scattering manifolds and microlocal singularities
Maciej ZWORSKI (カリフォルニア大学バークレイ校) 16:30-17:30
Local smoothing in the presence of lots of trapping
[ Reference URL ]
http://agusta.ms.u-tokyo.ac.jp/seminerphotos2/Zworski-abstract.pdf
伊藤健一 (東京大学大学院数理科学研究科) 15:00-16:00
Schr/"odinger equations on scattering manifolds and microlocal singularities
Maciej ZWORSKI (カリフォルニア大学バークレイ校) 16:30-17:30
Local smoothing in the presence of lots of trapping
[ Reference URL ]
http://agusta.ms.u-tokyo.ac.jp/seminerphotos2/Zworski-abstract.pdf
2008/01/22
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Serge Richard (Univ. Lyon 1)
Magnetic Schroedinger operators and twisted crossed product
Serge Richard (Univ. Lyon 1)
Magnetic Schroedinger operators and twisted crossed product
[ Abstract ]
During this seminar, we shall study spectral properties of generalized
magnetic Schroedinger operators H(B,V) with anisotropic magnetic field B
and scalar potential V. The essential spectrum of such operators is
expressed as a union of spectra of some asymptotic operators supported by
the quasi-orbits of a suitable dynamical system. A localization property
of the functional calculus of H(B,V) will also be presented. It directly
implies a non-propagation result for the unitary group generated by this
operator. The proofs rely on the use of twisted crossed product
C*-algebras. Twisted dynamical systems and their corresponding algebras
will be introduced and the natural link with magnetic Schroedinger
operators will be clearly established.
During this seminar, we shall study spectral properties of generalized
magnetic Schroedinger operators H(B,V) with anisotropic magnetic field B
and scalar potential V. The essential spectrum of such operators is
expressed as a union of spectra of some asymptotic operators supported by
the quasi-orbits of a suitable dynamical system. A localization property
of the functional calculus of H(B,V) will also be presented. It directly
implies a non-propagation result for the unitary group generated by this
operator. The proofs rely on the use of twisted crossed product
C*-algebras. Twisted dynamical systems and their corresponding algebras
will be introduced and the natural link with magnetic Schroedinger
operators will be clearly established.
2008/01/08
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Nikolay Tzvetkov (Lille大学)
On the restrictions of Laplace-Beltrami eigenfunctions to curves
Nikolay Tzvetkov (Lille大学)
On the restrictions of Laplace-Beltrami eigenfunctions to curves
