Nonradial Hörmander algebras of several variables and convolution operators

DOI10.1090/S0002-9947-01-02780-5zbMath0992.46020OpenAlexW1587258595MaRDI QIDQ2706612

José Bonet, Siegfried Momm, Antonio Galbis

Publication date: 20 March 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-01-02780-5

zbMATH Keywords

Fourier-Laplace transformconvolution operatorsurjectiveconvolution operatorsprincipal idealreal analytic functionsHörmander algebrasBeurling typeultradistributionultradifferential operatorspaces of quasianalytic functionsquasianalytic classRoumieu classquasianalytic weightspace of ultradifferentiable functions of Beurling type

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Operations with distributions and generalized functions (46F10) Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Entire functions of several complex variables (32A15) Rings and algebras of continuous, differentiable or analytic functions (46E25) Ideals and subalgebras (46H10) Algebras of holomorphic functions of several complex variables (32A38) PDEs of infinite order (35R50)

Related Items

Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non-quasianalytic classes ⋮ Non-quasianalytic curves in Fréchet spaces ⋮ The range of the restriction map for a multiplicity variety in Hörmander algebras of entire functions ⋮ Regularity of solutions of convolution equations ⋮ Solvability of convolution equations in the Beurling spaces of ultradifferentiable functions of mean type on an interval ⋮ Quasianalytic wave front sets for solutions of linear partial differential operators

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