Year: 2026
Type: article
Abstract: We establish two definitions of the convolution of vector measures on locally compact groups by employing injective tensor integration. These two formulations are shown to be isomorphic. We further investigate fundamental properties of the convolution of vector measures, including a representation in terms of double integrals and its behavior under the Fourier transform. In particular, we demonstrate that the Fourier transform of the convolution admits a factorization analogous to the classical case, with an inherent asymmetry arising from the vector-valued setting.
Source: Symmetry
DOI: 10.3390/sym18040668
Authors: Keng Wiboonton, Sorravit Phonrakkhet
Institutions: Chulalongkorn University, Walailak University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W7154580092
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