Analytic functions in the unit ball of bounded L-index in joint variables and of bounded L-index in direction: a connection between these classes

• Autorzy: Bandura Andriy , Skaskiv Oleh

Identyfikatory

DOI

10.1515/dema-2019-0008

• Języki publikacji: EN

Abstrakty

EN

We give negative answer to the question of Bordulyak and Sheremeta for more general classes of entire functions than in the original formulation: Does index boundedness in joint variables for an entire function F imply index boundedness in the variable zj for the function F? This question is addressed for entire functions of bounded L-index in joint variables and entire functions of bounded L-index in direction. We also present a class of analytic functions in the unit ball which has bounded L-index in joint variablesand has unbounded l-index in the variables z1 and z2 for any positive continuous function l : B2→C.

Słowa kluczowe

EN

bounded L-index in direction; entire function of several variables; bounded L-index in joint variables; analytic function in the unit ball; existence theorem

PL

funkcja całkowita; funkcje analityczne; twierdzenie o istnieniu

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 82--87
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Bandura Andriy

• Department of Advanced Mathematics, Ivano-Frankivsk National TechnicalUniversity of Oil and Gas, Ukraine, Postal address: 15 Karpatska street, Ivano-Frankivsk, 76019, Ukraine

autor

Skaskiv Oleh

• Department of Mathematics and Mechanics, Ivan Franko National University of L’viv, Ukraine, Postal address:1 Universytetska street, Lviv, 79000, Ukraine

Bibliografia

• [1] Bandura A., Skaskiv O., Entire functions of several variables of bounded index, Lviv, Publisher I. E. Chyzhykov, 2016
• [2] Bandura A., Skaskiv O., Entire functions of bounded L-index: Its zeros and behavior of partial logarithmic derivatives, J.Complex Analysis, 2017, Article ID 3253095, DOI: 10.1155/2017/3253095
• [3] Nuray F., Patterson R. F., Entire bivariate functions of exponential type, Bull. Math. Sci., 2015, 5(2), 171–177, DOI: 10.1007/s13373-015-0066-x
• [4] Nuray F., Patterson R. F., Multivalence of bivariate functions of bounded index, Le Matematiche, 2015, 70(2), 225–233, DOI: 10.4418/2015.70.2.14
• [5] Patterson R. F., Nuray F., A characterization of holomorphic bivariate functions of bounded index, Math. Slov., 2017, 67(3), 731–736, DOI: 10.1515/ms-2017-0005
• [6] Kuzyk A. D., Sheremeta M. M., Entire functions of bounded l-distribution of values, Math. Notes., 1986, 39(1), 3–8, DOI:10.1007/BF01647624
• [7] Lepson B., Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index, Proc. Sympos. Pure Math., 1968, 2, 298–307
• [8] Bordulyak M. T., Sheremeta M. M., Boundedness of the L-index of an entire function of several variables, Dopov. Akad. Nauk Ukr., 1993, 9, 10–13 (in Ukrainian)
• [9] Bandura A. I., Bordulyak M. T., Skaskiv O. B., Suflcient conditions of boundedness of L-index in joint variables, Mat. Stud., 2016, 45(1), 12–26, DOI: 10.15330/ms.45.1.12-26
• [10] Bandura A., Skaskiv O., Asymptotic estimates of entire functions of bounded L-index in joint variables, Novi Sad J. Math., 2018, 48(1), 103–116, DOI: 10.30755/NSJOM.06997
• [11] Bandura A. I., Skaskiv O. B., Directional logarithmic derivative and the distribution of zeros of an entire function of bounded L-index along the direction, Ukrain. Mat. J., 2017, 69(3), 500–508, DOI: 10.1007/s11253-017-1377-8
• [12] Bandura A. I., Skaskiv O. B., Iyer’s metric space, existence theorem and entire functions of bounded L-index in joint variables, Bukovyn. Mat. Zh., 2017, 5(3-4), 8–14 (in Ukrainian)
• [13] Pugh W. J., Sums of functions of bounded index, Proc. Amer. Math. Soc., 1969, 22, 319–323
• [14] Bandura A., Skaskiv O., Functions analytic in a unit ball of bounded L-index in joint variables, J. Math. Sci., 2017, 227(1), 1–12, DOI: 10.1007/s10958-017-3570-6
• [15] Bandura A. I., Skaskiv O. B., Analytic functions in the unit ball of bounded L-index: asymptotic and local properties, Mat. Stud., 2017, 48(1), 37–73, DOI: 10.15330/ms.48.1.37-73

Uwagi

PL

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