Sparsity of Gabor representation of Schrödinger propagators

DOI10.1016/j.acha.2008.08.003zbMath1171.35133OpenAlexW2069565717MaRDI QIDQ1012554

Fabio Nicola, Elena Cordero, Luigi Rodino

Publication date: 21 April 2009

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2008.08.003

zbMATH Keywords

Schrödinger equationmodulation spacesGabor framesshort-time Fourier transformFourier integral operators

Mathematics Subject Classification ID

Fourier integral operators applied to PDEs (35S30) Pseudodifferential operators (47G30) Numerical methods in Fourier analysis (65T99)

Related Items (31)

Boundedness of pseudodifferential operators with symbols in Wiener amalgam spaces on modulation spaces ⋮ Generalized metaplectic operators and the Schrödinger equation with a potential in the Sjöstrand class ⋮ Gabor frames of Gaussian beams for the Schrödinger equation ⋮ Semi-classical time-frequency analysis and applications ⋮ Modulation spaces and non-linear Hartree type equations ⋮ On exceptional times for pointwise convergence of integral kernels in Feynman-Trotter path integrals ⋮ An introduction to the Gabor wave front set ⋮ Gabor representations of evolution operators ⋮ Propagation of Gabor singularities for semilinear Schrödinger equations ⋮ Highly oscillatory unimodular Fourier multipliers on modulation spaces ⋮ Quasi-Banach algebras and Wiener properties for pseudodifferential and generalized metaplectic operators ⋮ Gabor frame decomposition of evolution operators and applications ⋮ Integral representations for the class of generalized metaplectic operators ⋮ Computing Fourier integral operators with caustics ⋮ The Cauchy problem for the Hartree type equation in modulation spaces ⋮ A Guide to Localized Frames and Applications to Galerkin-Like Representations of Operators ⋮ Kernel theorems for modulation spaces ⋮ Globally well and ill posedness for non-elliptic derivative Schrödinger equations with small rough data ⋮ The Gabor wave front set ⋮ Reconstruction of singularities for solutions of Schrödinger equations ⋮ Dispersion, spreading and sparsity of Gabor wave packets for metaplectic and Schrödinger operators ⋮ Approximation of Fourier integral operators by Gabor multipliers ⋮ The Cauchy problem for non-linear higher order Hartree type equation in modulation spaces ⋮ Boundedness of Schrödinger type propagators on modulation spaces ⋮ Exponentially sparse representations of Fourier integral operators ⋮ A characterization of modulation spaces by symplectic rotations ⋮ On the Continuity of $$\tau $$-Wigner Pseudodifferential Operators ⋮ On the existence of global solutions of the Hartree equation for initial data in the modulation space \(M^{p , q}(\mathbb{R})\) ⋮ Propagation of the Gabor wave front set for Schrödinger equations with non-smooth potentials ⋮ Schrödinger Equations in Modulation Spaces ⋮ A Multiscale Butterfly Algorithm for Multidimensional Fourier Integral Operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Modulation spaces \(M^{p,q}\) for \(0<p,q\leq\infty\)
• Sparse shearlet representation of Fourier integral operators
• Time-frequency analysis of Fourier integral operators
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Remarks on a Wiener type pseudodifferential algebra and Fourier integral operators
• Gabor frames and time-frequency analysis of distributions
• Curvelets and Fourier integral operators.
• Time-frequency analysis on modulation spaces \(M_{m}^{p,q}\), \(0 < p,q \leqslant \infty\).
• Nonlinear approximation with local Fourier bases
• Foundations of time-frequency analysis
• Some remarks on greedy algorithms
• Metaplectic representation on Wiener amalgam spaces and applications to the Schrödinger equation
• Fourier integral operators. I
• Fourier integral operators. II
• Fast Computation of Fourier Integral Operators
• Resolution of the wavefront set using continuous shearlets
• Harmonic Analysis in Phase Space. (AM-122)
• Wiener’s lemma for twisted convolution and Gabor frames
• Adaptive Wavelet Schemes for Nonlinear Variational Problems
• Coorbit space theory for quasi-Banach spaces
• The curvelet representation of wave propagators is optimally sparse

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