Generalized metaplectic operators and the Schrödinger equation with a potential in the Sjöstrand class

DOI10.1063/1.4892459zbMath1295.81050arXiv1306.5301OpenAlexW2050031419MaRDI QIDQ3189906

Luigi Rodino, Fabio Nicola, Elena Cordero, Karlheinz Gröchening

Publication date: 12 September 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.5301

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Groups and semigroups of linear operators (47D03) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Fourier integral operators applied to PDEs (35S30) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (33)

Convergence in \(L^{p}\) for Feynman path integrals ⋮ Boundedness of pseudodifferential operators with symbols in Wiener amalgam spaces on modulation spaces ⋮ Stability of Gabor frames under small time Hamiltonian evolutions ⋮ Semi-classical time-frequency analysis and applications ⋮ On exceptional times for pointwise convergence of integral kernels in Feynman-Trotter path integrals ⋮ Shubin type Fourier integral operators and evolution equations ⋮ On the pointwise convergence of the integral kernels in the Feynman-Trotter formula ⋮ Fractional Fourier transforms, harmonic oscillator propagators and Strichartz estimates on Pilipović and modulation spaces ⋮ Quasi-Banach algebras and Wiener properties for pseudodifferential and generalized metaplectic operators ⋮ Integral representations for the class of generalized metaplectic operators ⋮ Estimates on the modulation spaces for the Dirac equation with potential ⋮ Square-integrability of multivariate metaplectic wave-packet representations ⋮ Estimates on modulation spaces for Schrödinger evolution operators with quadratic and sub-quadratic potentials ⋮ Anisotropic Gevrey-Hörmander Pseudo-Differential Operators on Modulation Spaces ⋮ Linear Perturbations of the Wigner Transform and the Weyl Quantization ⋮ Reconstruction of singularities for solutions of Schrödinger equations ⋮ Dispersion, spreading and sparsity of Gabor wave packets for metaplectic and Schrödinger operators ⋮ Phase space analysis of semilinear parabolic equations ⋮ On the time slicing approximation of Feynman path integrals for non-smooth potentials ⋮ Almost diagonalization of \(\tau \)-pseudodifferential operators with symbols in Wiener amalgam and modulation spaces ⋮ On dissipative nonlinear evolutional pseudo-differential equations ⋮ Strichartz estimates for the metaplectic representation ⋮ Approximation of Feynman path integrals with non-smooth potentials ⋮ A characterization of modulation spaces by symplectic rotations ⋮ Weak-Type Estimates for the Metaplectic Representation Restricted to the Shearing and Dilation Subgroup of $$SL(2,\mathbb {R})$$ ⋮ On the Continuity of $$\tau $$-Wigner Pseudodifferential Operators ⋮ Almost Diagonalization of Pseudodifferential Operators ⋮ Propagation of the Gabor wave front set for Schrödinger equations with non-smooth potentials ⋮ Lagrangian distributions and Fourier integral operators with quadratic phase functions and Shubin amplitudes ⋮ Characterizations of some properties on weighted modulation and Wiener amalgam spaces ⋮ Characterisation of the Weyl-Hörmander classes by time-frequency shifts ⋮ Wave packet analysis of Schrödinger equations in analytic function spaces ⋮ Schrödinger equations with rough Hamiltonians

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Representation of Schrödinger operator of a free particle via short-time Fourier transform and its applications
• Banach spaces related to integrable group representations and their atomic decompositions. I
• Schatten-von Neumann properties for Fourier integral operators with non-smooth symbols. II
• The global Cauchy problem for the NLS and NLKG with small rough data
• Time-frequency analysis of Sjöstrand's class
• Unimodular Fourier multipliers for modulation spaces
• Time-frequency analysis of Fourier integral operators
• Boundedness of Schrödinger type propagators on modulation spaces
• Banach algebras of pseudodifferential operators and their almost diagonalization
• Sparsity of Gabor representation of Schrödinger propagators
• Remarks on a Wiener type pseudodifferential algebra and Fourier integral operators
• Foundations of time-frequency analysis
• Spaces of test functions via the STFT
• An algebra of pseudodifferential operators
• \(L^ p\)-mapping properties of functions of Schrödinger operators and their applications to scattering theory
• Wiener algebras of Fourier integral operators
• Estimates on modulation spaces for Schrödinger evolution operators with quadratic and sub-quadratic potentials
• Metaplectic representation on Wiener amalgam spaces and applications to the Schrödinger equation
• A short course on operator semigroups
• Schrödinger Equations in Modulation Spaces
• GEOMETRIC APPROACH TO THE HAMILTON–JACOBI EQUATION AND GLOBAL PARAMETRICES FOR THE SCHRÖDINGER PROPAGATOR
• Gabor representations of evolution operators
• Wiener’s Lemma: Theme and Variations. An Introduction to Spectral Invariance and Its Applications
• Evolution Equations and Generalized Fourier Integral Operators
• Symplectic Methods in Harmonic Analysis and in Mathematical Physics
• A Symbol Class for Some Schrodinger Equations on R n
• Harmonic Analysis in Phase Space. (AM-122)
• Estimations l²precisees pour des integrales oscillantes

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