PIP-Space Valued Reproducing Pairs of Measurable Functions

Camillo Trapani, Jean-Pierre Antoine

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We analyze the notion of reproducing pairs of weakly measurable functions, ageneralization of continuous frames. The aim is to represent elements of an abstract space Y assuperpositions of weakly measurable functions belonging to a space Z := Z(X, m), where (X, m) is ameasure space. Three cases are envisaged, with increasing generality: (i) Y and Z are both Hilbertspaces; (ii) Y is a Hilbert space, but Z is a PIP-space; (iii) Y and Z are both PIP-spaces. It is shown, inparticular, that the requirement that a pair of measurable functions be reproducing strongly constrainsthe structure of the initial space Y. Examples are presented for each case.
Original languageEnglish
Pages (from-to)52-
Number of pages22
JournalAxioms
Volume8
Publication statusPublished - 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics
  • Logic
  • Geometry and Topology

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