Some notes about distribution frame multipliers
Rosario Corso, Francesco Tschinke
TL;DR
This paper extends the concept of distribution frame multipliers to rigged Hilbert spaces, analyzing their properties and developing a symbolic calculus for Riesz distribution bases.
Contribution
It introduces a new framework for distribution frame multipliers in rigged Hilbert spaces and explores their properties and symbolic calculus for Riesz bases.
Findings
Conditions for domain density and boundedness are established.
A symbolic calculus for Riesz distribution bases is developed.
The extension broadens the applicability of multipliers in functional analysis.
Abstract
Inspired by a recent work about distribution frames, the definition of multiplier operator is extended in the rigged Hilbert spaces setting and a study of its main properties is carried on. In particular, conditions for the density of domain and boundedness are given. The case of Riesz distribution bases is examined in order to develop a symbolic calculus.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Digital Filter Design and Implementation · Advanced Harmonic Analysis Research