Hankel transforms in generalized Fock spaces
type: Item
instance of: scholarly article
title: Hankel transforms in generalized Fock spaces
zbMATH Open document ID: 0811.46033
DOI: 10.1155/S0161171294000384
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1994-06-19T00:00:00Z
full work available at URL: https://eudml.org/doc/47129
review text: Summary: A classical Fock space consists of functions of the form \(\varphi \leftrightarrow (\varphi_ 0, \varphi_ 1,\dots, \varphi_ q)\), where \(\varphi_ 0\in \mathbb{C}\) and \(\varphi_ q\in L^ p (\mathbb{R}^ q)\), \(q\geq 1\). We will replace the \(\varphi_ q\), \(q\geq 1\) with test functions having Hankel transforms. This space is a natural generalization of a classical Fock space as seen by expanding functionals having abstract Taylor series. The particular coefficients of such series are multilinear functionals having distributions as their domain. Convergence requirements set forth are somewhat in the spirit of ultra differentiable functions and ultra distribution theory. The Hankel transform oftentimes implemented in Cauchy problems will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the inductive limit parameter, \(s\), which sweeps out a scale of generalized Fock spaces.
Mathematics Subject Classification ID: 46F12
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 44A15
zbMATH DE Number: 569393
zbMATH Keywords: abelian theorems
zbMATH Keywords: Fock space
zbMATH Keywords: test functions having Hankel transforms
zbMATH Keywords: expanding functionals having abstract Taylor series
zbMATH Keywords: multilinear functionals having distributions as their domain
author: John Schmeelk
MaRDI profile type: Publication
OpenAlex ID: W2004804436
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description: scientific article; zbMATH DE number 569393