Slice holomorphic solutions of some directional differential equations with bounded L-index in the same direction

• Autorzy: Bandura Andriy , Skaskiv Oleh , Smolovyk Liana

Identyfikatory

DOI

10.1515/dema-2019-0043

• Języki publikacji: EN

Abstrakty

EN

In the paper we investigate slice holomorphic functions F : Cn→C having bounded L-index in a direction, i.e. these functions are entire on every slice {z0 +tb : t∈C} for an arbitrary z0∈Cn and for the fixed direction b∈Cn \ {0}, and (∃m0∈Z+) (∀m∈Z+) (∀z∈Cn) the following inequality holds [wzór], where L : Cn→R+ is a positive continuous function, [wzór] for p≥2. Also, we consider index boundedness in the direction of slice holomorphic solutions of some partial differentia equations with partial derivatives in the same direction. There are established sufficient conditions providing the boundedness of L-index in the same direction for every slie holomorphic solutions of these equations.

Słowa kluczowe

EN

bounded index; bounded L-index in direction; slice function; holomorphic function; bounded l-index; directional differential equation

PL

funkcja holomorficzna; równanie różniczkowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 482--489
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Bandura Andriy

• Department of Advanced Mathematics, Ivano-Frankivsk National Technical University of Oil and Gas, 15 Karpatska Street, Ivano-Frankivsk, 76019, Ukraine

autor

Skaskiv Oleh

• Department of Mathematics and Mechanics, Ivan Franko National University of L’viv, 1 Universytetska Street, Lviv, 79000, Ukraine

autor

Smolovyk Liana

• Department of Advanced Mathematics, Ivano-Frankivsk National Technical University of Oil and Gas, 15 Karpatska Street, Ivano-Frankivsk, 76019, Ukraine

Bibliografia

• [1] 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
• [2] 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))
• [3] Bandura A., Skaskiv O., Analog of Hayman’s theorem and its application to some system of linear partial differential equations, J. Math. Phys. Anal. Geom., 2019, 15(2), 170-191, DOI: 10.15407/mag15.02.170
• [4] Bordulyak M. T., On the growth of entire solutions of linear differential equations, Mat. Stud., 2000, 13(2), 219-223
• [5] Nuray F., Patterson R. F., Vector-valued bivariate entire functions of bounded index satisfying a system of differential equations, Mat. Stud., 2018, 49(1), 67-74, DOI: 10.15330/ms.49.1.67-74
• [6] Kuzyk A. D., Sheremeta M. N., Entire functions of boundedl-distribution of values, Math. Notes, 1986, 39(1), 3-8, DOI:10.1007/BF01647624
• [7] Kuzyk A. D., Sheremeta M. N., On entire functions, satisfying linear differential equations, Diff. Equations, 1990, 26(10), 1716-1722
• [8] Lepson B., Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index, Proc. Sympos. Pure Math., 1968, 2, 298-307
• [9] Macdonnell J. J., Some convergence theorems for Dirichlet-type series whose coeflcients are entire functions of bounded index, Doctoral dissertation, Catholic University of America, Washington, USA, 1957
• [10] Strelitz S., Asymptotic properties of entire transcendental solutions of algebraic differential equations, Contemp. Math.,1983, 25, 171-214, DOI: 10.1090/conm/025/730048
• [11] Sheremeta M., Analytic functions of bounded index, Lviv, VNTL Publishers, 1999
• [12] 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
• [13] Bandura A., Skaskiv O., Filevych P., Properties of entire solutions of some linear PDE’s, J. Appl. Math. Comput. Mech., 2017, 16(2), 17-28, DOI: 10.17512/jamcm.2017.2.02
• [14] Bandura A. I., Skaskiv O. B., Entire functions of bounded L-index in direction, Mat. Stud., 2007, 27(1), 30-52 (in Ukrainian)
• [15] Bandura A., New criteria of boundedness of L-index in joint variables for entire functions, Math. Bull. Shevchenko Sci. Soc., 2016, 13, 58-67 (in Ukrainian)

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).