Structure of the set of Borel exceptional vectors for entire curves

  • A.I. Bandura Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0003-0598-2237
  • Ya.I. Savchuk Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine
Keywords: entire curve, integral curve, Borel exceptional vector, Nevanlinna deficient vector, meromorphic function, admissible system of vectors.

Abstract

It is proved that the structure of the set of Borel exceptional vectors for transcendental entire curve something likes structure of the set of Nevanlinna
deficient vectors for entire curve of finite order.

Author Biography

A.I. Bandura, Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine

Professor of Department of Advanced Mathematics

References

Gol’dberg A. A., Some questions of the theory of distribution of values of meromorphic functions, in: G. Wittich, Latest Investigations on Single-Valued Analytic Functions, Fizmatgiz, Moscow (1960). (in Russian).

Gol’dberg A. A., Ostrovskii I. V., Value Distribution of Meromorphic Functions, Providence: AMS, 2008. (Translated from Russian ed. Moscow, Nauka, 1970).

Dektyarev I.M., Averaged deficiencies of holomorphic curves and divisors with an excessive deficiency value, Russian Mathematical Surveys, 44 (1989), №1, 237–238. https://doi.org/10.1070/RM1989v044n01ABEH002015

Mori S., Topics on meromorphic mappings and defects, Complex Var. Elliptic Equ., 56 (2011), №1-4, 363–373. https://doi.org/10.1080/17476930903394903

Petrenko V. P., Entire curves. Kharkiv: Vyshcha shkola, 1984.

Savchuk Ya. I., Structure of the set of defect vectors of entire and analytic curves of finite order, Ukr. Math. J., 37 (1985), №5, 494–499. https://doi.org/10.1007/BF01061174

Savchuk Ya. I., Set of deficient vectors of integral curves, Ukr. Math. J., 35 (1983), №3, 334–338. https://doi.org/10.1007/BF01092190

Savchuk Ya.I., Inverse problem of the theory of distribution of the values of entire and analytic curves, Journal of Soviet Mathematics, 48 (1990), №2, 220–231. https://doi.org/10.1007/BF01095801

Savchuk Ya.I., Valiron deficient vectors of entire curves of finite order, Journal of Soviet Mathematics, 52 (1990), №5, 3435–3437. https://doi.org/10.1007/BF01099913

Toda N., Holomorphic curves with an infinite number of deficiencies, Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), №6, 90–95. https://doi.org/10.3792/pjaa.80.90.

Published
2020-03-17
How to Cite
Bandura, A., & Savchuk, Y. (2020). Structure of the set of Borel exceptional vectors for entire curves. Matematychni Studii, 53(1), 41-47. https://doi.org/10.30970/ms.53.1.41-47
Section
Articles