BSU Bulletin. Mathematics, Informatics
Bibliographic description:
ABOUT COMPLETE DESCRIPTION OF THE WEIGHT CLASS OF ENTIRE FUNCTIONS // BSU Bulletin. Mathematics, Informatics. - 2019. №4. . - С. 3-11.
Title:
ABOUT COMPLETE DESCRIPTION OF THE WEIGHT CLASS OF ENTIRE FUNCTIONS
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Annotation:
Due to a number of well-known works by K. Weierstrass, J. Hadamard, E. Borel devoted to factorization of the classes of entire functions, the construction of factoriza- tion representations of different classes of functions continues to be relevant. Modern authors, such as M. M. Dzhrbashjan, W. Heyman, M. Tsuji, F. A. Shamoyan, A. Shirokov, B. N. Khabibullin, B. I. Korenblum, K. Seip, H. Hedenmalm successfully work in this field and publish their advances. The obtained factorization represen- tations of special classes of functions are used for solution of the problems of operator theory and approximation theory. A complete description of various functional classes includes both factorization and characterization of root sets. The article is devoted to the construction of a representation of the class of entire functions of the complex variable with weight from Lp-spaces. We prove our assertions using the methods of complex and functional analysis.
Keywords:
factorization representation; entire function; root sets; continued prod- uct; factor; order of entire function; complete description; plane of complex numbers; counting function; estimate.
List of references:
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Shamoyan F. A., Shubabko E. N. Vvedenie v teoriyu vesovykh Lp-klassov me- romorfnykh funktsii [Introduction to the Theory of Weighted Lp-Classes of Meromorphic Functions]. Bryansk, 2009. 152 p.
Okhlupina O. V. Obobshchenie odnoi teoremy Valirona na sluchai subgarmo- nicheskikh funktsii [Generalization of a Theorem of Valiron in the Case of Subharmonic Functions]. Vestnik Bryanskogo gosudarstvennogo universiteta. Tochnye i estestvennye nauki. Bryansk: Buryat State University Publ., 2012. No. 4(2). P. 34–44.
Okhlupina O. V. Potentsialy tipa Grina i integralnye predstavleniya vesovykh klassov subgarmonicheskikh funktsii [Green-Type Potentials and Integral Representa- tions of Weight Classes of Subharmonic Functions]. Cand. phys. and math. sci. diss. Bryansk, 2012. 118 p.
Okhlupina O. V. Obobshchenie odnoi teoremy Valirona na sluchai tselykh funktsii [Generalization of a Theorem of Valiron for the Cases of Entire Functions]. Vestnik Bryanskogo gosudarstvennogo universiteta: Pedagogika. Psikhologiya. Is- toriya. Pravo. Literaturovedenie. Yazykoznanie. Ekonomika. Tochnye i estestvennye nauki. Bryansk: Bryansk State University Publ., 2015. No 3(26). Pp. 400–408.
Shamoyan F. A. Parametricheskoe predstavlenie i opisanie kornevykh mnoz- hestv vesovykh klassov golomorfnykh v kruge funktsii [Parametric Representation and Description of the Root Sets of Weight classes of Holomorphic in the Circle Func- tions]. Siberian Mathematical Journal. 1999. Vol. 40. No 6. P. 1422–1440.
Shamoyan F. A., Shubabko E. N. Vvedenie v teoriyu vesovykh Lp-klassov me- romorfnykh funktsii [Introduction to the Theory of Weighted Lp-Classes of Meromorphic Functions]. Bryansk, 2009. 152 p.
Okhlupina O. V. Obobshchenie odnoi teoremy Valirona na sluchai subgarmo- nicheskikh funktsii [Generalization of a Theorem of Valiron in the Case of Subharmonic Functions]. Vestnik Bryanskogo gosudarstvennogo universiteta. Tochnye i estestvennye nauki. Bryansk: Buryat State University Publ., 2012. No. 4(2). P. 34–44.
Okhlupina O. V. Potentsialy tipa Grina i integralnye predstavleniya vesovykh klassov subgarmonicheskikh funktsii [Green-Type Potentials and Integral Representa- tions of Weight Classes of Subharmonic Functions]. Cand. phys. and math. sci. diss. Bryansk, 2012. 118 p.
Okhlupina O. V. Obobshchenie odnoi teoremy Valirona na sluchai tselykh funktsii [Generalization of a Theorem of Valiron for the Cases of Entire Functions]. Vestnik Bryanskogo gosudarstvennogo universiteta: Pedagogika. Psikhologiya. Is- toriya. Pravo. Literaturovedenie. Yazykoznanie. Ekonomika. Tochnye i estestvennye nauki. Bryansk: Bryansk State University Publ., 2015. No 3(26). Pp. 400–408.
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