2024 : 11 : 9
Mohammad Reza Azimi

Mohammad Reza Azimi

Academic rank: Associate Professor
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Education: PhD.
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Research

Title
Universal family of translations on weighted Orlicz spaces
Type
JournalPaper
Keywords
Orlicz space · Locally compact group · Weight function · Young function · Universal family · Orbit · Translation · Convolution · Hypercyclic
Year
2022
Journal POSITIVITY
DOI
Researchers ، Mohammad Reza Azimi

Abstract

Let G be a locally compact group, be a Young function and ω be a weight on G. An associated weighted Orlicz space is denoted by L(G, ω). For any S ⊆ G, a family of left translations {Ls}s∈S on L(G, ω), defined by Ls f (t) := f (s−1t) for all t ∈ G, is said S-universal if there exists a function f ∈ L(G, ω), called an S-universal vector, such that its S-orbit, namely, OrbS( f ) = {Ls( f ) : s ∈ S} is dense in L(G, ω). In this paper, first it is shown that any compact group G, does not admit an S-universal vector in L(G, ω) and only the infinite dimensional weighted Orlicz spaces L(G, ω) may contain it. In the sequel, under natural restrictions, the existence of S-universal vector leads to find out that G must be second countable. Moreover, we give a necessary and sufficient condition for {Ls}s∈S to be S-universal on L(G, ω). At last, some other sp