Geodesic
Comparison Tauberian theorems and hyperbolic operators with constant coefficients
Ufa mathematical journal, Tome 7 (2015) no. 3, pp. 47-53 Cet article a éte moissonné depuis la source Math-Net.Ru

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As comparison Tauberian theorems one usually means theorems which by a prescribed asymptotic behavior of the ratio of some integral transforms of two (generalized) functions make a conclusion on asymptotic behavior of other integral transformations of these functions. In the work we prove the comparison Tauberian function for the generalized functions whose Laplace transform have a bounded argument. In particular, examples of these functions are the kernels and the fundamental solutions of differential operators with constant coefficients hyperbolic w.r.t. a cone.
Keywords: generalized functions, Tauberian theorems, quasi-asymptotics, operators hyperbolic w.r.t. a cone. 
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Yu. N. Drozhzhinov; B. I. Zavialov. Comparison Tauberian theorems and hyperbolic operators with constant coefficients. Ufa mathematical journal, Tome 7 (2015) no. 3, pp. 47-53. http://geodesic.mathdoc.fr/item/UFA_2015_7_3_a5/

[1] Kostyuchenko A. G., Sargsyan I. S., Raspredelenie sobstvennykh znachenii, Nauka, M., 1979 | MR

[2] Vladimirov V. S., Drozhzhinov Yu. N., Zavyalov B. I., Mnogomernye tauberovy teoremy dlya obobschennykh funktsii, Nauka, M., 1986 | MR

[3] Drozhzhinov Yu. N., Zavyalov B. I., “Mnogomernye tauberovy teoremy sravneniya dlya obobschennykh funktsii v konusakh”, Matem. sb., 126(168):4 (1985), 515–542 | MR | Zbl

[4] Drozhzhinov Yu. N., Zavyalov B. I., “Mnogomernye abelevy i tauberovy teoremy sravneniya”, Matem. sb., 180:9 (1989), 1234–1258 | MR | Zbl

[5] Drozhzhinov Yu. N., Zavyalov B. I., “Mnogomernye tauberovy teoremy sravneniya dlya golomorfnykh funktsii ogranichennogo argumenta”, Izvestiya AN SSSR, ser. matem., 55:6 (1991), 1139–1155 | MR | Zbl

[6] Vladimirov V. S., Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979 | MR

[7] Seneta E., Pravilno menyayuschiesya funktsii, Nauka, M., 1985 | MR

[8] Yakymiv A. L., Veroyatnostnye prilozheniya tauberovykh teorem, Fizmatlit, M., 2005

[9] Boimatov K. Kh., “Mnogomernye spektralnye asimptotiki ellipticheskikh operatorov v oblastyakh, udovletvoryayuschikh usloviyu konusa”, DAN SSSR, 316:1 (1991), 14–18 | MR

[10] Drozhzhinov Yu. N., Zavyalov B. I., “Obobschennye funktsii asimptoticheski odnorodnye vdol traektorii neustoichivogo vyrozhdennogo uzla”, Vestnik Samarskogo gos. tekhn. un-ta, ser. fiz-mat. nauki, 2011, no. 1(22), 68–82 | DOI

[11] Drozhzhinov Yu. N., Zavyalov B. I., “Obobschennye funktsii asimptoticheski odnorodnye po traektoriyam, opredelyaemym odnoparametricheskimi gruppami”, Izvestiya RAN, ser. matematicheskaya, 76:3 (2012), 39–92 | DOI | MR | Zbl