Vector valued hyperfunctions and boundary values of vector valued harmonic and holomorphic functions

DOI10.2977/prims/1231263781zbMath1177.46028OpenAlexW1970120392MaRDI QIDQ1011985

Michael Langenbruch, Paweł Domański

Publication date: 14 April 2009

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1231263781

zbMATH Keywords

boundary values of vector valued harmonic functionsboundary values of vector valued holomorphic functionspartial differential operators on vector valued spaces of smooth functionsvector valued harmonic functionsvector valued hyperfunctions

Mathematics Subject Classification ID

Hyperfunctions, analytic functionals (46F15) General theory of PDEs and systems of PDEs with constant coefficients (35E20) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Hyperfunctions (32A45) Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) (46M18) Hypoelliptic equations (35H10) Distributions and ultradistributions as boundary values of analytic functions (46F20) Topological invariants ((DN), ((Omega)), etc.) for locally convex spaces (46A63) Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) (35R20) Calculus of functions taking values in infinite-dimensional spaces (26E20)

Related Items (10)

Asymptotic Fourier and Laplace transforms for vector-valued hyperfunctions ⋮ Parameter dependence of solutions of the Cauchy-Riemann equation on weighted spaces of smooth functions ⋮ On the Laplace transform for vector valued hyperfunctions ⋮ On the abstract Cauchy problem for operators in locally convex spaces ⋮ Weighted spaces of vector-valued functions and the \(\varepsilon\)-product ⋮ Real analytic parameter dependence of solutions of differential equations over Roumieu classes ⋮ Real analytic parameter dependence of solutions of differential equations ⋮ Global right inverses for Euler type differential operators on the space of smooth functions ⋮ The abstract Cauchy problem in locally convex spaces ⋮ The inhomogeneous Cauchy-Riemann equation for weighted smooth vector-valued functions on strips with holes

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