# Translation-invariant operators in reproducing kernel Hilbert spaces

@inproceedings{HerreraYanez2021TranslationinvariantOI, title={Translation-invariant operators in reproducing kernel Hilbert spaces}, author={Crispin Herrera-Yanez and E. Maximenko and Gerardo Ramos-Vazquez}, year={2021} }

Let G be a locally compact abelian group with a Haar measure, and Y be a measure space. Suppose that H is a reproducing kernel Hilbert space of functions on G× Y , such that H is naturally embedded into L2(G× Y ) and is invariant under the translations associated with the elements of G. Under some additional technical assumptions, we study the W*-algebra V of translation-invariant bounded linear operators acting on H . First, we decompose V into the direct integral of the W*-algebras of bounded… Expand

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