Invertibility of Convolution Operator in $L_{p}$ Spaces in Applications to $R$-semigroups

M. V. Vdovin

Ural State University, Pr. Lenina 51, Ekaterinburg, 620083

Abstract: Sufficient conditions for existence of an inverse operator to convolution operator in $L_ {p}(\mathbb{R}),\ p\in(2,\infty)$, spaces and sufficient conditions for density of the convolution operator range are obtained. These convolution operator properties considered in applications to a wide class of regularizing semigroups — to $R$-semigroups.

Keywords: convolution operator; $L_{p}$ spaces; invertibility of convolution operator; $R$-semigroup; regularization method.

UDC: 517.983:517.956:517.444