Geodesic
The Cauchy problem for evolution equations with the Bessel operator of infinite order.~I
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2010), pp. 3-15.

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We establish necessary and sufficient conditions under which the Bessel operator of infinite order is bounded in certain spaces. We study properties of the Bessel transformations of distributions from these spaces, those of convolutions, convolutors, and multiplicators.
Mots-clés : Bessel transformation, distributions
Keywords: Bessel operator of infinite order, convolutors, multiplicators. 
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V. V. Gorodestkii; O. V. Martynyuk. The Cauchy problem for evolution equations with the Bessel operator of infinite order.~I. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2010), pp. 3-15. http://geodesic.mathdoc.fr/item/IVM_2010_6_a0/

[1] Matiichuk M. I., Parabolichni singulyarni kraiovi zadachi, In-t matematiki NAN Ukraïni, Kiïv, 1999, 176 pp.

[2] Krekhivskii V. V., “Teoremy edinstvennosti reshenii zadachi Koshi dlya uravnenii s operatorom Besselya”, Matematicheskoe modelirovanie fizicheskikh protsessov, In-t matematiki AN USSR, Kiev, 1989, 82–86 | MR

[3] Ivasishen S. D., Lavrenchuk V. P., “Ob integralnom predstavlenii reshenii parabolicheskoi sistemy s operatorom Besselya”, Nelineinye granichnye zadachi, 1992, no. 4, 19–25 | MR

[4] Verenich I. I., “Vnutrennie otsenki reshenii parabolicheskikh uravnenii s operatorom Besselya”, DAN USSR, 1977, no. 11, 969–974 | Zbl

[5] Zhitomirskii Ya. I., “Zadacha Koshi dlya sistem lineinykh uravnenii v chastnykh proizvodnykh s differentsialnym operatorom Besselya”, Matem. sb., 36(78):2 (1955), 299–310 | MR | Zbl

[6] Gorodetskii V. V., Granichni vlastivosti gladkikh u shari rozv'yazkiv rivnyan parabolichnogo tipu, Ruta, Chernivtsi, 1998, 225 pp.

[7] Gorodetskii V. V., Zhitaryuk I. V., “Zadacha Koshi dlya odnogo klasu parabolichnikh sistem z operatorom Besselya v prostorakh uzagalnenikh funktsii”, Dop. AN URSR, 1991, no. 7, 20–23 | MR

[8] Gorodetskii V. V., Zhitaryuk I. V., Lavrenchuk V. P., Zadacha Koshi dlya lineinykh parabolicheskikh uravnenii s operatorom Besselya v prostranstvakh obobschennykh funktsii tipa $S'$, Rus. Dep. v UkrINTEI 09.03.93, No 338, Uk93, Chernovitskii universitet, Chernovtsy, 1993, 29 pp., Bibliogr. 10 nazv.

[9] Gelfand I. M., Shilov G. E., Nekotorye voprosy teorii differentsialnykh uravnenii, Fizmatgiz, M., 1958, 274 pp. | MR

[10] Gurevich B. L., “Nekotorye prostranstva osnovnykh i obobschennykh funktsii i problema Koshi dlya konechno-raznostnykh sistem”, DAN SSSR, 99:6 (1954), 893–896

[11] Korn T., Korn G., Spravochnik po matematike, Nauka, M., 1977, 832 pp. | MR

[12] Levitan B. I., “Razlozhenie po funktsiyam Besselya v ryady i integraly Fure”, UMN, 6:2 (1951), 102–143 | MR | Zbl