Eigenfunction expansions of ultradifferentiable functions and ultradistributions in \(\mathbb R^n\)

DOI10.1007/s11868-016-0157-9zbMath1384.46030arXiv1512.01684OpenAlexW2195456389MaRDI QIDQ2401487

Jasson Vindas, Đorđe Vučković

Publication date: 1 September 2017

Published in: Journal of Pseudo-Differential Operators and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.01684

zbMATH Keywords

ultradifferentiable functionsultradistributionsGelfand-Shilov spaceseigenfunction expansionsDenjoy-Carleman classesShubin-type differential operators

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Pseudodifferential operators as generalizations of partial differential operators (35S05) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Topological linear spaces of test functions, distributions and ultradistributions (46F05)

Related Items (11)

A sequential approach to the convolution of Roumieu ultradistributions ⋮ Eigenfunction expansions of ultradifferentiable functions and ultradistributions. III: Hilbert spaces and universality ⋮ Ultradistributional boundary values of harmonic functions on the sphere ⋮ Relations between Hermite and Laguerre expansions of ultradistributions over \(\mathbb R^d\) and \(\mathbb R^d_+\) ⋮ Global regularity of Weyl pseudo-differential operators with radial symbols in each phase-space variable ⋮ The nuclearity of Gelfand-Shilov spaces and kernel theorems ⋮ Eigenfunction expansions of ultradifferentiable functions and ultradistributions. II. Tensor representations ⋮ Infinite order \(\Psi\mathrm{DOs}\): composition with entire functions, new Shubin-Sobolev spaces, and index theorem ⋮ Infinite Order Pseudo-Differential Operators ⋮ Anisotropic Shubin operators and eigenfunction expansions in Gelfand-Shilov spaces ⋮ Modulation spaces associated with tensor products of amalgam spaces

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