\(G\)-type spaces of ultradistributions over \(\mathbb {R}^d_+\) and the Weyl pseudo-differential operators with radial symbols

DOI10.1007/s13398-016-0313-3zbMath1419.35265arXiv1602.04017OpenAlexW2963748634MaRDI QIDQ2412807

Smiljana Jakšić, Bojan Prangoski, Stevan Pilipović

Publication date: 27 October 2017

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.04017

zbMATH Keywords

Laguerre expansionspseudo-differential operators with radial symbolsspaces of ultradistributions over \(\mathbb {R}^d_+\)

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Integral transforms in distribution spaces (46F12) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Integral operators (47G10) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Pseudodifferential operators (47G30)

Related Items (7)

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 ⋮ Images of function and distribution spaces under the Bargmann transform ⋮ Estimates of pseudo-differential operators associated with fractional Hankel transform on the space of type S ⋮ Localization of Fréchet frames and expansion of generalized functions ⋮ Spectral properties of Landau Hamiltonians with non-local potentials ⋮ Norm estimates for the pseudo-differential operator involving fractional Hankel-like transform on \(\mathcal{S}\)-type spaces

Cites Work

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• Gelfand-Shilov spaces for the Hankel transform
• Weyl transforms
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• A bound on the Laguerre polynomials
• Gelfand–Shilov Type Spaces Through Hermite Expansions
• Classes of Degenerate Elliptic Operators in Gelfand-Shilov Spaces
• Generalization of Zemanian Spaces of Generalized Functions which Have Orthonormal Series Expansions
• Laguerre Series as Boundary Values
• The Analytic Functionals in the Lower Half Plane as a Gel'fand-Shilov Space
• Extension theorem of Whitney type for S(Rd+) by use of the Kernel theorem

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