Topological properties of convolutor spaces via the short-time Fourier transform

DOI10.1090/tran/8080zbMath1468.46004arXiv1801.09246OpenAlexW3097892340MaRDI QIDQ5143145

Jasson Vindas, Andreas Debrouwere

Publication date: 11 January 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.09246

zbMATH Keywords

Gelfand-Shilov spacesshort-time Fourier transformcompleteness of inductive limitsconvolutor spaces

Mathematics Subject Classification ID

Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) 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 linear spaces of test functions, distributions and ultradistributions (46F05)

Related Items (9)

Explicit commutative sequence space representations of function and distribution spaces on the real half-line ⋮ Weighted (\textit{PLB})-spaces of ultradifferentiable functions and multiplier spaces ⋮ Sequence space representations for spaces of smooth functions and distributions via Wilson bases ⋮ Microlocal analysis for Gelfand-Shilov spaces ⋮ Projective descriptions of spaces of functions and distributions ⋮ Convolution on distribution spaces characterized by regularization ⋮ Inclusion theorems for the Moyal multiplier algebras of generalized Gelfand-Shilov spaces ⋮ Convolutors of translation-modulation invariant Banach spaces of ultradistributions ⋮ Extension of localisation operators to ultradistributional symbols with super-exponential growth

Cites Work

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• A sequence space representation of L. Schwartz' space \({{\mathcal{O}_{C}}}\)
• New distribution spaces associated to translation-invariant Banach spaces
• Characterization of L. Schwartz' convolutor and multiplier spaces \(\mathcal O'_C\) and \(\mathcal O_M\) by the short-time Fourier transform
• Théorie des distributions à valeurs vectorielles
• Note on the \(n\)-dimensional tempered ultra distributions
• Foundations of time-frequency analysis
• Convolvability and regularization of distributions
• Ultradifferentiable functions and Fourier analysis
• Derived functors in functional analysis
• Some remarks concerning the spaces of multipliers and convolutors, \({\mathcal{O}_M}\) and \(\mathcal{O}^\prime_C\), of Laurent Schwartz
• A new proof for the bornologicity of the space of slowly increasing functions
• On the spaces \(\mathcal O_C^m\) of John Horváth
• A comparison of two different ways to define classes of ultradifferentiable functions
• Ultradifferentiable Functions on Compact Intervals
• [https://portal.mardi4nfdi.de/wiki/Publication:3210373 On the Topology of the Space of Convolution Operators in K � M]
• Extension operators for spaces of infinite differentiable Whitney jets
• A Projective Description of Weighted Inductive Limits
• On the functors Ext¹(E,F) for Fréchet spaces
• [https://portal.mardi4nfdi.de/wiki/Publication:4122395 Hypoelliptic Convolution Equations in  � p , p > 1]
• On duals of weakly acyclic $(LF)$-spaces
• On Completeness and Projective Descriptions of Weighted Inductive Limits of Spaces of Fréchet-Valued Continuous Functions
• Weighted (LF)‐spaces of Continuous Functions
• The short-time Fourier transform of distributions of exponential type and tauberian theorems for shift-asymptotics
• On weighted inductive limits of spaces of ultradifferentiable functions and their duals
• On convolution in weighted DLp′-spaces
• On the space of convolution operators in $K'_{1}$
• Homological methods in the theory of locally convex spaces
• Acyclic inductive spectra of Fréchet spaces
• Produits tensoriels topologiques et espaces nucléaires

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