Invertibility of Convolution Operator in $L_{p}$ Spaces in Applications to $R$-semigroups
The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 3, pp. 54-67
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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.
@article{IIGUM_2011_4_3_a4,
author = {M. V. Vdovin},
title = {Invertibility of {Convolution} {Operator} in $L_{p}$ {Spaces} in {Applications} to $R$-semigroups},
journal = {The Bulletin of Irkutsk State University. Series Mathematics},
pages = {54--67},
publisher = {mathdoc},
volume = {4},
number = {3},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IIGUM_2011_4_3_a4/}
}
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M. V. Vdovin. Invertibility of Convolution Operator in $L_{p}$ Spaces in Applications to $R$-semigroups. The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 3, pp. 54-67. http://geodesic.mathdoc.fr/item/IIGUM_2011_4_3_a4/