On the algebra of integral operators with involution

A. G. Baskakov ; G. V. Garkavenko ; N. B. Uskova

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 1, Tome 230 (2023), pp. 41-49.

Résumé

In this paper, we consider integral operators with kernels depending on the sum and difference of arguments in the space $L_p(\mathbb{R})$, $p\in[1, \infty)$. We prove that such operators form a subalgebra of the algebra of bounded linear operators. The study of operators with kernels depending on the difference of arguments was carried out using Banach $L_1(\mathbb{Z})$-modules. The differences and similarities between the subalgebra of integral operators and the corresponding subalgebra of difference operators with involution are noted.

Détail

Keywords: integral operator, involution, Banach module, difference operator, spectrum
Mots-clés : semi-Carleman kernel, convolution

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