Generalized Fourier expansions for zero-solutions of surjective convolution operators on \({\mathcal D}_\{\omega\}({\mathbb{R}})'\)

DOI10.1007/BF01199116zbMath0674.46021OpenAlexW2790785317MaRDI QIDQ1121488

Rüdiger W. Braun, Reinhold Meise

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1007/bf01199116

zbMATH Keywords

Fourier-Laplace transform(DFN)-space of Gevrey-ultradistributions of exponent dabsolute basis of exponential solutionsomega-ultradistributions of Roumieu typepower space in the sense of Zaharjutasequence space representationssurjective convolution operators

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) 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)

Related Items

Extremal plurisubharmonic functions of linear growth on algebraic varieties, The existence and the continuation of holomorphic solutions for convolution equations in tube domains, Continuous Linear Right Inverses for Partial Differential Operators on Non ‐ Quasianalytic Classes and on Ultradistributions, Phragmén-Lindelöf principles on algebraic varieties, 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, \(\omega\)-fundamental solutions supported in a half space, Generalized Fourier expansion in kernels of convolution operators on Fourier hyperfunctions, On Hankel Transform and Hankel Convolution of Beurling Type Distributions Having Upper Bounded Support

Cites Work

• Almost analytic extension of ultradifferentiable functions and the boundary values of holomorphic functions
• A new look at interpolation theory for entire functions of one variable
• Die Nuklearität der Ultradistributionsräume und der Satz vom Kern. I
• Ultradifferentiable functions and Fourier analysis
• La transformation de Fourier complexe et l'équation de convolution
• Sur quelques extensions de la notion de distribution
• Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals.
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