SUM AND PRODUCT OF FUNCTIONS HAVING BOUNDED L-INDEX IN A DIRECTION WHICH ARE SLICE HOLOMORPHIC IN THE SAME DIRECTION

Authors

  • A. I. Bandura Ivano-Frankivsk National Technical University of Oil and Gas
  • O. B. Skaskiv Ivan Franko National University of L'viv

DOI:

https://doi.org/10.31471/2304-7399-2019-1(53)-9-20

Keywords:

bounded index, bounded L-index in direction, slice function, holomorphic function, bounded l-index, sum.

Abstract

Our objects of investigations are sum and product of holomorphic function of bounded index. There are established sufficient conditions providing the boundedness of L-index in the same direction for these operations. In particular, the multiplication of functions from this class is closed operation.

References

Bandura A., Skaskiv O., Slice Holomorphic Functions in Several Variables with Bounded L-Index in Direction, Axioms, 2019, 8(3), Article ID 88, DOI: 10.3390/axioms8030088

Bandura A.I., Skaskiv O.B., Some criteria of boundedness of L-index in a direction for slice holomorphic functions of several complex variables, Ukr. Matem. Visn., 2019, 16(2), 154–180 Engl. transl.: J. Math. Sci. (in print)

Bandura A., Skaskiv O., Smolovyk L., Slice holomorphic solutions of some directional differential equations with bounded L-index in the same direction, Demonstratio Math. (in print)

Bandura A.I., Skaskiv O.B., Entire functions of bounded L-index in direction, Mat. Stud., 2007, 27(1), 30–52 (in Ukrainian)

Bandura A.I., Sum of entire functions of bounded L-index in direction, Mat. Stud., 2016, 45(2), 149–158, DOI: 10.15330/ms.45.2.149-158

Bandura A., Skaskiv O., Boundedness of the L-index in a direction of entire solutions of second order partial differential equation, Acta Comment. Univ. Tartu. Math., 2018, 22(2), 223–234, DOI: 10.12697/ACUTM.2018.22.18

Bandura A.I., Product of two entire functions of bounded L-index in direction is a function with the same class, Bukovyn. Mat. Zh., 2016, 4 (1-2), 8–12

Kuzyk A.D., Sheremeta M.N., Entire functions of bounded l-distribution of values, Math. Notes, 1986, 39 (1), 3–8, DOI: 10.1007/BF01647624

Kuzyk A.D., Sheremeta, M.N., On entire functions, satisfying linear differential equations, Diff. equations, 1990, 26(10), 1716–1722

Lepson B., Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index, Proc. Sympos. Pure Math., 1968, 2, 298–307

Macdonnell J.J., Some convergence theorems for Dirichlet-type series whose coefficients are entire functions of bounded index, Doctoral dissertation, Catholic University of America, Washington, USA, 1957

Strelitz S., Asymptotic properties of entire transcendental solutions of algebraic differential equations, Contemp. Math., 1983, 25, 171–214, DOI: 10.1090/conm/025/730048

Sheremeta M., Analytic functions of bounded index, Lviv, VNTL Publishers, 1999

Pugh W.J., Sums of functions of bounded index, Proc. Amer. Math. Soc., 1969, 22, 319-323

Downloads

Published

2019-09-27

How to Cite

Bandura, A. I. ., & Skaskiv, O. B. . (2019). SUM AND PRODUCT OF FUNCTIONS HAVING BOUNDED L-INDEX IN A DIRECTION WHICH ARE SLICE HOLOMORPHIC IN THE SAME DIRECTION. PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, (1(53), 9–20. https://doi.org/10.31471/2304-7399-2019-1(53)-9-20