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W W "Schrödinger Operators and Related Topics"

172wK@wXyNg_Z~i[

F2019 N 7 6 iyj 15:00 -- 17:30
ꏊF wK@w@42K 205Z~i[

1. 15:00--16:00
u: @đ iEj

TitleF$$L^2$$ boundedness of pseudodifferential operators on manifolds with end

Abstract: We introduce pseudodifferential operators acting on functions or half-densities on a manifold with end. In the asymtotically hyperbolic case, we have not yet obtained the decay of integral kernel of our pseudodifferential operators in off-diagonal because of the exponential increasing of the coefficients of the metric tensor in the polar coordinate near infinity. In spite of this difficulty, we can prove $$L^2$$ boundedness of the pseudodifferential operators with bounded symbols by the same method as that of usual pseudodifferential operators on Euclidean spaces. As an application, we construct the parametrices of differential operators on manifolds with end and estimate the error term in the $$L^2$$ operator norm.

16:00--16:30 tea time

2. 16:30--17:30
u: @Vp iEj

Title: On a continuum limit of discrete Schrödinger operators on square lattice@

AbstractF {uł́Aiq̗UV[fBK[pf̘AɌɂēꂽʂ񍐂B̓Iɂ́Aiq߂ĂɌŗUV[fBK[pfAԏ̃V[fBK[pfɃm]xg邱ƂAUԂƘAԂ̊Ԃ̓K؂ȑΉ^邱ƂŏؖB̌ʂ̉pƂāAV[fBK[pf̗UŗLlyтɕtŗL֐̑QߋUV[fBK[pf瓾A̎x̏ォ̕]B{͒@iwK@wjƂ̋łB

171wK@wXyNg_Z~i[

F2019 N 6 22 iyj 15:00 -- 17:30
ꏊF wK@w@42K 205Z~i[

1. 15:00--16:00
u: T@Y iEj

TitleFSemiclassical shape resonances for Stark Hamiltonian

Abstract: We discuss semiclassical resonances for the Stark Hamiltonian. The main results are the Weyl law and the resonance expansion of the propagator in the shape resonance model. We introduce the complex distortion outside a cone to define and study Stark resonances for non-globally analytic potentials without energy range restriction. To prove the resonance expansion, we also discuss the functional pseudodifferential calculus for the Stark Hamiltonian.

16:00--16:30 tea time

2. 16:30--17:30
u: O@k iwj

Title: Semiclassical methods and observability estimate for Schrödinger operators with homogeneous potentials of order zero@

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170wK@wXyNg_Z~i[

F2019 N 6 8 iyj 15:00 -- 17:30
ꏊF wK@w@42K 205Z~i[

1. 15:00--16:00
u: J@Ǝ iEj

TitleFA remark on wave operators on the scale of Sobolev spaces

Abstract: VfBK[̎U_ɂāAgpf݂̑ƑQߊS͉̑Qߋ肷 dvȐłBU_ł͔gpf $$L^2$$ Œ邱ƂقƂǂł邪A Uɉpۂɂ̓\{tԂł̍l@RƕKvɂȂB̍uł́A ́iCjgpf\{tԏ̋ɌƂđ݂đQߊSł邽߂̏\ ̃|eVUւ̉pɂďЉBႦ1K̃\{tԂ̏ꍇA ̏͗ՊEȓِZ^A炩Ȓ^A1f^^_ݍpȂ L͈͂̃|eVɓKpłBԂΐĎ\{tԂ̏ꍇЉB

16:00--16:30 tea time

2. 16:30--17:30
u: @m i}g喼_j

Title: Continuum limit of scattering solutions for periodic lattices@

AbstractFConsider the Helmholtz equation on periodic lattices. By the scattering solution, we mean the one associated with the continuous spectrum satisfying the radiation condition. For a class of lattices including the square, triangular and hexagonal lattices, we show that, as the mesh size tends to 0, the scattering solution converges to that for the continuous model. This is a joint work with Arne Jensen in Aalborg.

169wK@wXyNg_Z~i[

F2019 N 5 18 iyj 15:00 -- 17:30
ꏊF wK@w@42K 205Z~i[

1. 15:00--16:00
u: 㓡@䂫ݎ iwK@Ej

TitleFBinding of Atoms in Mueller theory

16:00--16:30 tea time

2. 16:30--17:30
u: bc@ iwK@Ej

Title: dq̃n~gjǍŗLl̉E]@

AbstractF̓dqƌqjꍇ̃V[fBK[ɑ΂ẮA܂qjŒ肵ēdq̌ŗLllƂ@܂B̌ŗLl͌ɂ͉Ȃ߁AŗLl̕]@l܂BSdq̃n~gjA͉LEłAŗLl̏E]ɂmin-maxɊÂ@܂BŁAŗLl̉E]Grosse-Hertel-Thirring̕@ɂ΁A1dqn~gjǍŗLlɋA܂BǍŗLlɂ͉AŗLl̉E]͓ɂȂ܂B{uł́A1dqn~gjǍŗLl̉E]^̕@񍐂܂B

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• shu.nakamuraiƁjgakushuin.ac.jp i@)
• fumihikoiƁjmath.gakushuin.ac.jpijFj