On the Inverse to the Harmonic Oscillator

DOI10.1080/03605302.2015.1007145zbMath1318.35091arXiv1306.6866OpenAlexW2027072078MaRDI QIDQ5256317

Joachim Toft, Marco Cappiello, Luigi Rodino

Publication date: 22 June 2015

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.6866

zbMATH Keywords

ultradistributionsinverseharmonic oscillatorGelfand-Shilov estimates

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) A priori estimates in context of PDEs (35B45) Asymptotic expansions of solutions to PDEs (35C20) PDEs in connection with quantum mechanics (35Q40) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Generalized function theory (30Gxx)

Related Items (7)

Generalized Mehler formula for time-dependent non-selfadjoint quadratic operators and propagation of singularities ⋮ Uncertainty principle via variational calculus on modulation spaces ⋮ Shubin type Fourier integral operators and evolution equations ⋮ Fractional Fourier transforms, harmonic oscillator propagators and Strichartz estimates on Pilipović and modulation spaces ⋮ On the Weyl symbol of the resolvent of the harmonic oscillator ⋮ Quantization of Gaussians ⋮ Lagrangian distributions and Fourier integral operators with quadratic phase functions and Shubin amplitudes

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• Pseudo-differential operators and Gevrey classes
• Sub-Exponential Decay and Uniform Holomorphic Extensions for Semilinear Pseudodifferential Equations
• Generalization of Zemanian Spaces of Generalized Functions which Have Orthonormal Series Expansions

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