The structure of spaces of quasianalytic functions of Roumieu type

DOI10.1007/S00013-007-2073-YzbMath1147.46024OpenAlexW2001386519MaRDI QIDQ2474120

José Bonet, Paweł Domański

Publication date: 5 March 2008

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-007-2073-y

zbMATH Keywords

solvabilitydependence on parametersconvolution operatorsplitting of short exact sequenceslinear partial differential operatorspace of real analytic functionsPLS-spacevector valued equationspace of ultradifferentiable functions of Roumieu type

Mathematics Subject Classification ID

Topological linear spaces of continuous, differentiable or analytic functions (46E10) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) (46M18) 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) Quasi-analytic and other classes of functions of one complex variable (30D60)

Related Items (10)

On subadditivity-like conditions for associated weight functions ⋮ Solution to the first Cousin problem for vector-valued quasianalytic functions ⋮ Parameter dependence of solutions of the Cauchy-Riemann equation on weighted spaces of smooth functions ⋮ Real analytic parameter dependence of solutions of differential equations over Roumieu classes ⋮ Splitting and parameter dependence in the category of \(\mathrm{PLH}\) spaces ⋮ The splitting of exact sequences of PLS-spaces and smooth dependence of solutions of linear partial differential equations ⋮ Weighted PLB-spaces of continuous functions arising as tensor products of a Fréchet and a DF-space ⋮ Geometric characterization of interpolation in the space of Fourier-Laplace transforms of ultradistributions of Roumieu type ⋮ Real analytic parameter dependence of solutions of differential equations ⋮ A linear topological invariant for spaces of quasianalytic functions of Roumieu type

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