A. V. Keller, J. K. Al-Delfi, “Holomorphic degenerate groups of operators in quasi-Banach spaces”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 7:1 (2015), 20

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Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika"

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Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika", 2015, Volume 7, Issue 1, Pages 20–27 (Mi vyurm206)

This article is cited in 13 scientific papers (total in 14 papers)

Mathematics

Holomorphic degenerate groups of operators in quasi-Banach spaces

A. V. Keller, J. K. Al-Delfi

South Ural State University

Full-text PDF (259 kB) Citations (14)

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Abstract: Probably, Sobolev type equations, i.e. unsolved with respect to the highest derivative, first appeared in the late nineteenth century. Due to the fact that the interest to the Sobolev type equations recently significantly increased, the need arose for their consideration in quasi-Banach spaces. Specifically, this study aimed at understanding non-classical models of mathematical physics in quasi-Banach spaces.
The theory of holomorphic degenerate groups of operators, developed in Banach spaces and Frechet spaces is transferred to quasi-Banach spaces. Abstract results are illustrated by specific examples.
The article besides the introduction and the references contains three parts. The first part provides the necessary information regarding the theory of relatively $p$-bounded operators in quasi-Banach spaces. The second one represents the construction of the holomorphic group of solving operators. The third part contains the sufficient conditions for pair of operators to generate group of solving operators.

Keywords: degenerate groups of operators; quasi-Banach spaces; Sobolev type equations.

Received: 15.01.2015

Bibliographic databases:

Document Type: Article

UDC: 517.9

Language: Russian

Citation: A. V. Keller, J. K. Al-Delfi, “Holomorphic degenerate groups of operators in quasi-Banach spaces”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 7:1 (2015), 20–27

Citation in format AMSBIB

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\by A.~V.~Keller, J.~K.~Al-Delfi

\paper Holomorphic degenerate groups of operators in quasi-Banach spaces

\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.

\yr 2015

\vol 7

\issue 1

\pages 20--27

\mathnet{http://mi.mathnet.ru/vyurm206}

\elib{https://elibrary.ru/item.asp?id=22856977}

Linking options:

https://www.mathnet.ru/eng/vyurm206

https://www.mathnet.ru/eng/vyurm/v7/i1/p20

This publication is cited in the following 14 articles:

A. V. Keller, “O napravleniyakh issledovanii uravnenii sobolevskogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 16:4 (2023), 5–32
M. A. Sagadeeva, “Vyrozhdennye potoki razreshayuschikh operatorov dlya nestatsionarnykh uravnenii sobolevskogo tipa”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 9:1 (2017), 22–30
E. M. Buryak, T. K. Plyshevskaya, A. B. Samarov, “Seminaru po uravneniyam sobolevskogo tipa chetvert veka”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:1 (2017), 165–169
F. L. Hasan, “The bounded solutions on a semiaxis for the linearized Hoff equation in quasi-Sobolev spaces”, J. Comp. Eng. Math., 4:1 (2017), 27–37
K. V. Vasyuchkova, N. A. Manakova, G. A. Sviridyuk, “Some mathematical models with a relatively bounded operator and additive “white noise” in spaces of sequences”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:4 (2017), 5–14
J. K. T. Al-Isawi, “On kernels and images of resolving analytic degenerate semigroups in quasi-Sobolev spaces”, J. Comp. Eng. Math., 3:1 (2016), 10–19
E. V. Bychkov, Ya. O. Al'-Ani, “A linearized model of vibrations in the DNA molecule in the quasi-Banach spaces”, J. Comp. Eng. Math., 3:1 (2016), 20–26
G. A. Sviridyuk, N. A. Manakova, “The Barenblatt – Zheltov – Kochina model with additive white noise in quasi-Sobolev spaces”, J. Comp. Eng. Math., 3:1 (2016), 61–67
M. A. Sagadeeva, “Mathematical bases of optimal measurements theory in nonstationary case”, J. Comp. Eng. Math., 3:3 (2016), 19–32
M. A. Sagadeeva, F. L. Khasan, “Ogranichennye resheniya modeli Barenblatta–Zheltova–Kochinoi v kvazisobolevykh prostranstvakh”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:4 (2015), 138–144
M. A. Sagadeeva, F. L. Khasan, “Suschestvovanie invariantnykh podprostranstv i eksponentsialnykh dikhotomii reshenii dinamicheskikh uravnenii sobolevskogo tipa v kvazibanakhovykh prostranstvakh”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:4 (2015), 46–53
F. L. Hasan, “Solvability of initial problems for one class of dynamical equations in quasi-Sobolev spaces”, J. Comp. Eng. Math., 2:3 (2015), 34–42
M. A. Sagadeeva, A. S. Rashid, “Existence of solutions in quasi-Banach spaces for evolutionary Sobolev type equations in relatively radial case”, J. Comp. Eng. Math., 2:2 (2015), 71–81
A. V. Keller, A. A. Zamyshlyaeva, M. A. Sagadeeva, “On integration in quasi-Banach spaces of sequences”, J. Comp. Eng. Math., 2:1 (2015), 52–56

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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