Some remarks concerning the spaces of multipliers and convolutors, \({\mathcal{O}_M}\) and \(\mathcal{O}^\prime_C\), of Laurent Schwartz

DOI10.1007/s13398-012-0059-5zbMath1276.46029OpenAlexW1966986029MaRDI QIDQ1935071

Julian Larcher

Publication date: 30 January 2013

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://doi.org/10.1007/s13398-012-0059-5

zbMATH Keywords

inductive limitmultiplierscompact embeddingsprojective limittempered distributionsSchwartz spaceultrabornologicalconvolutors

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) 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 (4)

Spectra and ergodic properties of multiplication and convolution operators on the space \(\mathcal{S}(\mathbb{R})\) ⋮ Topologies in the Set of Rapidly Decreasing Distributions ⋮ Topological properties of convolutor spaces via the short-time Fourier transform ⋮ Convolutors on \(\mathcal{S}_{\omega}(\mathbb{R}^N)\)

Cites Work

• Espaces de fonctions différentiables à valeurs vectorielles
• Théorie des distributions à valeurs vectorielles
• The spaces \({\mathcal O}_ M\) and \({\mathcal O}_ C\) are ultrabornological. A new proof
• A note on the spaces \({\mathcal O}_ M\) and \({\mathcal O}'_ M\)
• A representation of the space \(O_ M\).
• The topology on certain spaces of multipliers of temperate distributions
• Weighted Sobolev embedding with unbounded and decaying radial potentials
• Einführung in die Theorie der lokalkonvexen Räume
• Projective and injective limits of weakly compact sequences of locally convex spaces
• Compactness in L 2 and the Fourier Transform
• Produits tensoriels topologiques et espaces nucléaires
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