Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii, v. 2, Prostranstva osnovnykh i obobschennykh funktsii, Fizmatgiz, M., 1958, 308 pp. | MR

[2] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii, v. 3, Nekotorye voprosy teorii differentsialnykh uravnenii, Fizmatgiz, M., 1958, 275 pp. | MR

[3] A. Zigmund, Trigonometricheskie ryady, v. 2, Mir, M., 1965, 538 pp. | MR

[4] V. K. Ivanov, I. V. Melnikova, A. I. Filinkov, Differentsialno-operatornye uravneniya i nekorrektnye zadachi, Nauka, M., 1995, 176 pp. | MR

[5] I. V. Melnikova, “Polugruppovaya regulyarizatsiya differentsialnykh zadach”, Dokl. RAN, 393:6 (2003), 1–5 | MR

[6] I. V. Melnikova, M. V. Vdovin, “Regulyarizatsiya nekorrektnykh differentsialnykh zadach Koshi v prostranstvakh $L_{p}(\mathbb{R})$, $p\geq1$”, Proceedings of the Seventeenth Crimean autumn mathematical school-symposium, Spectral and Evolution Problems, 17, 2007, 56–64

[7] I. P. Natanson, Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974, 480 pp. | MR

[8] S. M. Nikolskii, Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977, 456 pp. | MR

[9] I. V. Melnikova, Q. Zheng, J. Zhang, “Regularization of weakly ill-posed Cauchy problems”, Journal of Inverse and Ill-Posed Problems, 10:5 (2002) | DOI | MR

[10] I. V. Melnikova, U. A. Anufrieva, “Peculiarities and regularization of ill-posed Cauchy problems with differential operators”, Journal of Mathematical Sciences, 148:4 (2008), 481–632 | DOI | MR