Product of hyperfunctions on the circle
type: Item
instance of: scholarly article
title: Product of hyperfunctions on the circle
zbMATH Open document ID: 0964.32005
DOI: 10.1007/BF02773222
author: Yanyan Li
published in: Israel Journal of Mathematics
publication date: 2000-09-19T00:00:00Z
review text: Let \(HF(T)\) be the set of all hyperfunctions on the unit circle \(T\). These objects can be interpreted as natural generalisations of Schwartz distributions on \(T\). The product of two hyperfunctions \(\varphi\in HF(T)\) and \(\psi\in HF(T)\) makes sense if it is possible to compute in some sense the convolution \(\widehat\varphi *\widehat\psi\) and if the sequence \(((\widehat\varphi *\widehat\psi) (n))_{n\in \mathbb{Z}}\) is the sequence of Fourier coefficients of some hyperfunction which the authors call the product of \(\varphi\) and \(\psi\). Let \(\varphi\) and \(\psi\) be two hyperfunctions on the circle which have disjoint support. Then the authors interpret in terms of Fourier coefficients the fact that their product, defined in the sense of sheaf theory, vanishes.
reviewed by: Gandikota L. N. Rao
Mathematics Subject Classification ID: 32A45
Mathematics Subject Classification ID: 32C35
Mathematics Subject Classification ID: 58J15
Mathematics Subject Classification ID: 46F15
zbMATH DE Number: 1445784
zbMATH Keywords: product of hyperfunctions
zbMATH Keywords: hyperfunctions
zbMATH Keywords: circle
zbMATH Keywords: sheaf theory
MaRDI profile type: Publication
cites work: Q4378580
cites work: Q4839148
cites work: On Fourier transforms of measures with compact support
cites work: Q4398315
cites work: Singular inner functions and biinvariant subspaces for dissymmetric weighted shifts
cites work: Sous-espaces invariants par translations bilatérales de certains espaces de Hilbert de suites quasi-analytiquement pondérées
cites work: Q4533150
cites work: Asymptotically holomorphic functions and translation invariant subspaces of weighted Hilbert spaces of sequences
description: scientific article; zbMATH DE number 1445784