The abstract Cauchy problem in locally convex spaces

DOI10.1007/S13398-022-01295-5zbMath1496.34028arXiv2112.02677OpenAlexW4286423587MaRDI QIDQ2081202

Karsten Kruse

Publication date: 12 October 2022

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/2112.02677

zbMATH Keywords

abstract Cauchy problemhyperfunctionasymptotic resolventasymptotic Laplace transform

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Spectrum, resolvent (47A10) Laplace transform (44A10) Hyperfunctions, analytic functionals (46F15)

Cites Work

• Strongly continuous and locally equi-continuous semigroups on locally convex spaces
• On the Laplace transform for vector valued hyperfunctions
• Functional analysis and related topics, 1991. Proceedings ot the international conference in memory of Professor Kôsaku Yosida held at RIMS, Kyoto University, Japan, July 29-Aug. 2, 1991
• Semi-groups of operators in Fréchet space and applications to partial differential equations
• Perturbation for a class of transition semigroups on the Hölder space \(C_{b,\mathrm{loc}}^{\theta}(H)\)
• On Fourier transforms of distribution semigroups
• Vector valued hyperfunctions and boundary values of vector valued harmonic and holomorphic functions
• \(C_ 0\)-semigroups on a locally convex space
• On the theory of semigroups of operators on locally convex spaces
• The Cauchy problem for higher-order abstract differential equations
• Quasi-distribution semigroups and integrated semigroups
• The analysis of linear partial differential operators. I: Distribution theory and Fourier analysis.
• Holomorphic functional calculus for operators on a locally convex space
• A Hille-Yosida theorem for bi-continuous semigroups
• Hille-Yosida theory in convenient analysis.
• On the abstract Cauchy problem for operators in locally convex spaces
• On equicontinuity and tightness of bi-continuous semigroups
• The inhomogeneous Cauchy-Riemann equation for weighted smooth vector-valued functions on strips with holes
• Asymptotic Fourier and Laplace transforms for vector-valued hyperfunctions
• \(C_0\)-sequentially equicontinuous semigroups
• The splitting of exact sequences of PLS-spaces and smooth dependence of solutions of linear partial differential equations
• Semigroups of operators in locally convex spaces
• Problèmes de Cauchy abstraits et applications à quelques problèmes mixtes
• Continuity and equicontinuity of semigroups on norming dual pairs
• Aufbaukurs Funktionalanalysis und Operatortheorie
• Asymptotic Fourier and Laplace transformations for hyperfunctions
• Distribution semigroups and abstract Cauchy problems
• One-Parameter Semigroups for Linear Evolution Equations
• Chebyshev-Haar systems in the theory of discontinuous Kellogg kernels
• Desch‐Schappacher perturbation of one‐parameter semigroups on locally convex spaces
• Generation of equicontinuous semigroups by hermitian and sectorial operators. I
• Hyperfunction solutions of the abstract Cauchy problem
• Semigroups of Operators on Locally Convex Spaces
• Dissipative operators and additive perturbations in locally convex spaces
• Measure and integration theory
• Semi-groups of operators in locally convex spaces
• Semi-groups of operators in locally convex spaces
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