Distribution semigroups and abstract Cauchy problems

DOI10.1090/S0002-9947-99-02035-8zbMath0983.47028OpenAlexW1586033451MaRDI QIDQ4219183

Peer Christian Kunstmann

Publication date: 18 November 1998

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02035-8

zbMATH Keywords

convolution operatordistribution semigroupsregularized semigrouplocal integrated semigroupnon-densely defined generators

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Operations with distributions and generalized functions (46F10) Spectrum, resolvent (47A10) Linear differential equations in abstract spaces (34G10) Integrated semigroups (47D62)

Related Items (20)

On Fourier transforms of distribution semigroups ⋮ Frequently hypercyclic $C$-distribution semigroups and their generalizations ⋮ \(C\)-distribution semigroups and \(C\)-ultradistribution semigroups in locally convex spaces ⋮ Degenerate $C$-ultradistribution semigroups in locally convex spaces ⋮ Differential and analytical properties of semigroups of operators ⋮ On the abstract Cauchy problem for operators in locally convex spaces ⋮ Unnamed Item ⋮ Sharp extensions for convoluted solutions of abstract Cauchy problems ⋮ Rational approximation schemes for bi-continuous semigroups ⋮ Spectral properties of pseudo-resolvents under structured perturbations ⋮ Convoluted \(C\)-cosine functions and semigroups. Relations with ultradistribution and hyperfunction sines ⋮ Rational inversion of the Laplace transform ⋮ Ultradistribution semigroups ⋮ Hyperfunction semigroups ⋮ Rational approximation schemes for solutions of the first and second order Cauchy problem ⋮ Quasi-equicontinous exponential families of generalized function \(C\)-semigroups in locally convex spaces ⋮ The abstract Cauchy problem in locally convex spaces ⋮ Degenerate C-distribution cosine functions and degenerate C-ultradistribution cosine functions in locally convex spaces ⋮ Structural theorems for ultradistribution semigroups ⋮ On a solution of the Cauchy problem in the weighted spaces of Beurling ultradistributions

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