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過去の記録 ～05/01｜次回の予定｜今後の予定 05/02～
| 開催情報 | 火曜日 16:00～17:30 数理科学研究科棟(駒場) 156号室 |
|---|---|
| 担当者 | 石毛 和弘, 坂井 秀隆, 伊藤 健一 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/analysis/ |
過去の記録
2011年10月11日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
和田出 秀光 氏 (早稲田大学(日本学術振興会特別研究員PD))
重み付きTrudinger-Moser型不等式の最良定数に関して (JAPANESE)
和田出 秀光 氏 (早稲田大学(日本学術振興会特別研究員PD))
重み付きTrudinger-Moser型不等式の最良定数に関して (JAPANESE)
[ 講演概要 ]
同講演では、斉次重み付きTrudinger-Moser型不等式を
最良定数と共に考察する。
重みなしの場合は、 Adachi -Tanaka, Proc. Amer. Math. Soc. (1999),
により全空間上のスケール不変なTrudinger-Moser型不等式が
最良定数と共に導出されており、我々は重み付きTrudinger-Moser型
不等式への拡張を試みる。
更に、重み付きTrudinger-Moser型不等式の偏微分方程式への
応用として、重み付き指数型非線形項を伴うKlein-Gordon方程式を
2次元で考察し、同方程式の局所解及び大域解の存在を証明する。
同講演では、斉次重み付きTrudinger-Moser型不等式を
最良定数と共に考察する。
重みなしの場合は、 Adachi -Tanaka, Proc. Amer. Math. Soc. (1999),
により全空間上のスケール不変なTrudinger-Moser型不等式が
最良定数と共に導出されており、我々は重み付きTrudinger-Moser型
不等式への拡張を試みる。
更に、重み付きTrudinger-Moser型不等式の偏微分方程式への
応用として、重み付き指数型非線形項を伴うKlein-Gordon方程式を
2次元で考察し、同方程式の局所解及び大域解の存在を証明する。
2011年07月12日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
小林 政晴 氏 (東京理科大学)
The inclusion relation between Sobolev and modulation spaces (JAPANESE)
小林 政晴 氏 (東京理科大学)
The inclusion relation between Sobolev and modulation spaces (JAPANESE)
[ 講演概要 ]
In this talk, we consider the inclusion relations between the $L^p$-Sobolev spaces and the modulation spaces. As an application, we give mapping properties of unimodular Fourier multiplier $e^{i|D|^\\alpha}$ between $L^p$-Sobolev spaces and modulation spaces.
Joint work with Mitsuru Sugimoto (Nagoya University).
In this talk, we consider the inclusion relations between the $L^p$-Sobolev spaces and the modulation spaces. As an application, we give mapping properties of unimodular Fourier multiplier $e^{i|D|^\\alpha}$ between $L^p$-Sobolev spaces and modulation spaces.
Joint work with Mitsuru Sugimoto (Nagoya University).
2011年04月26日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
片岡 清臣 氏 (東京大学大学院数理科学研究科)
On the system of fifth-order differential equations which describes surfaces containing six continuous families of circles (JAPANESE)
片岡 清臣 氏 (東京大学大学院数理科学研究科)
On the system of fifth-order differential equations which describes surfaces containing six continuous families of circles (JAPANESE)
2010年11月16日(火)
16:00-18:30 数理科学研究科棟(駒場) 123号室
GCOE miniworkshopと合同
打越敬祐 氏 (防衛大学) 16:00-16:45
Hyperfunctions and vortex sheets (ENGLISH)
L. Boutet de Monvel 氏 (University of Paris 6) 17:00-18:30
Residual trace and equivariant asymptotic trace of Toeplitz operators (ENGLISH)
GCOE miniworkshopと合同
打越敬祐 氏 (防衛大学) 16:00-16:45
Hyperfunctions and vortex sheets (ENGLISH)
L. Boutet de Monvel 氏 (University of Paris 6) 17:00-18:30
Residual trace and equivariant asymptotic trace of Toeplitz operators (ENGLISH)
2010年09月28日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
Pavel Exner 氏 (Czech Academy of Sciences)
Some spectral and resonance properties of quantum graphs (ENGLISH)
Pavel Exner 氏 (Czech Academy of Sciences)
Some spectral and resonance properties of quantum graphs (ENGLISH)
[ 講演概要 ]
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年07月13日(火)
17:00-18:00 数理科学研究科棟(駒場) 128号室
Carlos Villegas Blas 氏 (メキシコ国立自治大学)
On a limiting eigenvalue distribution theorem for perturbations of the hydrogen atom (JAPANESE)
Carlos Villegas Blas 氏 (メキシコ国立自治大学)
On a limiting eigenvalue distribution theorem for perturbations of the hydrogen atom (JAPANESE)
[ 講演概要 ]
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年06月22日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
Ivana Alexandrova 氏 (East Carolina University)
Resonances for Magnetic Scattering by Two Solenoidal Fields at Large Separation (ENGLISH)
Ivana Alexandrova 氏 (East Carolina University)
Resonances for Magnetic Scattering by Two Solenoidal Fields at Large Separation (ENGLISH)
[ 講演概要 ]
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年06月15日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
滝口 孝志 氏 (防衛大学校 数学教育室)
Sato's counterexample and the structure of generalized functions (JAPANESE)
滝口 孝志 氏 (防衛大学校 数学教育室)
Sato's counterexample and the structure of generalized functions (JAPANESE)
[ 講演概要 ]
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年04月13日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
Jean-Marc Bouclet 氏 (トゥールーズ大学,フランス)
Strichartz estimates and the Isozaki-Kitada parametrix
on asymptotically hyperbolic manifolds (ENGLISH)
Jean-Marc Bouclet 氏 (トゥールーズ大学,フランス)
Strichartz estimates and the Isozaki-Kitada parametrix
on asymptotically hyperbolic manifolds (ENGLISH)
2010年01月26日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
Jacob S. Christiansen 氏 (コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)
Jacob S. Christiansen 氏 (コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)
2010年01月19日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
岡田 靖則 氏 (千葉大・理)
超函数の有界性と Massera 型定理について
岡田 靖則 氏 (千葉大・理)
超函数の有界性と Massera 型定理について
2009年11月24日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
吉野 邦生 氏 (東京都市大学)
Analytic Properties of Eigen Values of Daubechies Localization Operator
吉野 邦生 氏 (東京都市大学)
Analytic Properties of Eigen Values of Daubechies Localization Operator
[ 講演概要 ]
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年09月15日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
打越 敬祐 氏 (防衛大学校数学教育室)
渦層の超局所解析
打越 敬祐 氏 (防衛大学校数学教育室)
渦層の超局所解析
[ 講演概要 ]
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年07月21日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
Georgi Raikov 氏 (PUC, Chile)
Low Energy Asymptotics of the SSF for Pauli Operators with Non-Constant Magnetic Fields
Georgi Raikov 氏 (PUC, Chile)
Low Energy Asymptotics of the SSF for Pauli Operators with Non-Constant Magnetic Fields
[ 講演概要 ]
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年06月30日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
Ivana Alexandrova 氏 (東京大数理)
The Structure of the Scattering Amplitude for Schrodinger Operators with a Strong Magnetic Field
Ivana Alexandrova 氏 (東京大数理)
The Structure of the Scattering Amplitude for Schrodinger Operators with a Strong Magnetic Field
[ 講演概要 ]
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年06月02日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
神本 晋吾 氏 (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 氏 (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年05月26日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
Myriam Ounaies 氏 (Strasbourg大学数学科)
Intrepolation problems in H￥"ormander algebras
Myriam Ounaies 氏 (Strasbourg大学数学科)
Intrepolation problems in H￥"ormander algebras
[ 講演概要 ]
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年04月28日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
下村 明洋 氏 (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 氏 (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年01月20日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
吉野 邦生 氏 (武蔵工業大学)
Generating function of eigenvalues of Daubechies Localization Operator
吉野 邦生 氏 (武蔵工業大学)
Generating function of eigenvalues of Daubechies Localization Operator
[ 講演概要 ]
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年01月12日(月)
16:30-18:00 数理科学研究科棟(駒場) 128号室
Jacob S. Christiansen
氏 (コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)
Jacob S. Christiansen
氏 (コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)
2008年11月25日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
Ovidiu Calin 氏 (Eastern Michigan University)
Heat kernels for subelliptic operators
Ovidiu Calin 氏 (Eastern Michigan University)
Heat kernels for subelliptic operators
[ 講演概要 ]
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年11月11日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
新國 裕昭 氏 (首都大学東京)
Rotation number approach to spectral analysis of the generalized Kronig-Penney Hamiltonians
新國 裕昭 氏 (首都大学東京)
Rotation number approach to spectral analysis of the generalized Kronig-Penney Hamiltonians
2008年10月28日(火)
17:00-18:00 数理科学研究科棟(駒場) 123号室
いつもと時間、場所が異なります。またこの日から3日間連続講演となります。第2回、第3回はそれぞれ29, 30日に同じ部屋、時間帯で行われます。
Serge Alinhac 氏 (パリ大学オルセイ校)
Introduction to geometric analysis of hyperbolic equations
いつもと時間、場所が異なります。またこの日から3日間連続講演となります。第2回、第3回はそれぞれ29, 30日に同じ部屋、時間帯で行われます。
Serge Alinhac 氏 (パリ大学オルセイ校)
Introduction to geometric analysis of hyperbolic equations
2008年10月14日(火)
16:00-17:30 数理科学研究科棟(駒場) 002号室
GCOE講演会と共催です.部屋と時間が通常と異なりますのでご注意ください
George Sell 氏 (ミネソタ大学)
Thin 3D Navier-Stokes equations: Ultimate boundedness of solutions with large data and global attractors
GCOE講演会と共催です.部屋と時間が通常と異なりますのでご注意ください
George Sell 氏 (ミネソタ大学)
Thin 3D Navier-Stokes equations: Ultimate boundedness of solutions with large data and global attractors
[ 講演概要 ]
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年05月20日(火)
16:30-18:00 数理科学研究科棟(駒場) 128号室
Vania Sordoni 氏 (ボローニャ大学)
Wave operators for diatomic molecules
Vania Sordoni 氏 (ボローニャ大学)
Wave operators for diatomic molecules
