On Beurling measure algebras. (English) Zbl 07613029

Stokke, Ross

Commentat. Math. Univ. Carol. 63, No. 2, 169-187 (2022).

Summary: We show how the measure theory of regular compacted-Borel measures defined on the \(\delta\)-ring of compacted-Borel subsets of a weighted locally compact group \((G,\omega)\) provides a compatible framework for defining the corresponding Beurling measure algebra \(\mathcal{M}(G,\omega)\), thus filling a gap in the literature.

MSC:

43A10	Measure algebras on groups, semigroups, etc.
22D15	Group algebras of locally compact groups
43A05	Measures on groups and semigroups, etc.
43A20	\(L^1\)-algebras on groups, semigroups, etc.
43A60	Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
28C10	Set functions and measures on topological groups or semigroups, Haar measures, invariant measures

Keywords:

weighted locally compact group; group algebra; measure algebra; Beurling algebra