Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-index in Joint Variables

Vita Baksa; Andriy Bandura; Oleh Skaskıv

doi:10.33205/cma.650977

Research Article

Year 2020, Volume: 3 Issue: 1, 9 - 19, 01.03.2020

Vita Baksa Andriy Bandura , Oleh Skaskıv

https://doi.org/10.33205/cma.650977

Cited By: 1

Abstract

References

V.P. Baksa: Analytic vector-functions in the unit ball having bounded $ L $-index in joint variables. Carpathian Math. Publ. 11 (2) (2019), 213-227. doi 10.15330/cmp.11.2.213-227
V.P. Baksa, A.I. Bandura, O.B. Skaskiv: Analogs of Fricke's theorems for analytic vector-valued functions in the unit ball having bounded $ L $-index in joint variables. submitted to Proceedings of IAMM of NASU.
V.P. Baksa, A.I. Bandura, O.B. Skaskiv: Analogs of Hayman's theorem and of logarithmic criterion for analytic vector-valued functions in the unit ball having bounded $ L $-index in joint variables. submitted to Matematica Slovaca.
A. I. Bandura, O. B. Skaskiv: Analytic functions in the unit ball of bounded $ L $-index asymptotic and local properties. Mat. Stud. 48 (1) (2017), 37-73. doi 10.15330/ms.48.1.37-73.
A. Bandura, O. Skaskiv: Sufficient conditions of boundedness of $L$-index and analog of Hayman's Theorem for analytic functions in a ball. Stud. Univ. Babec s-Bolyai Math. 63(4) (2018), 483-501. doi 10.24193/subbmath.2018.4.06.
A. Bandura, O. Skaskiv: Functions analytic in the unit ball having bounded L-index in a direction. Rocky Mountain J. Math. 49 (4) (2019), 1063-1092. doi 10.1216/RMJ-2019-49-4-1063.
A. Bandura, O. Skaskiv: Asymptotic estimates of entire functions of bounded $ L $-index in joint variables. Novi Sad J. Math. 48(1) (2018), 103-116. doi 10.30755/NSJOM.06997.
A. Bandura, N. Petrechko, O. Skaskiv: Maximum modulus in a bidisc of analytic functions of bounded $ L $ -index and an analogue of Hayman's theorem. Matem. Bohem. 143(4) (2018), 339-354. doi 10.21136/MB.2017.0110-16.
A.I. Bandura, O.B. Skaskiv, V.L. Tsvigun: Some characteristic properties of analytic functions in $D\times C$ of bounded $L$-index in joint variables. Bukovyn. Mat. Zh. 6 (1-2) (2018), 21-31. doi 10.31861/bmj2018.01.021.
A.I. Bandura, N.V. Petrechko, O.B. Skaskiv: Analytic in a polydisc functions of bounded $L $ -index in joint variables. Mat. Stud. 46 (1) (2016), 72-80. doi 10.15330/ms.46.1.72-80.
A. Bandura, O. Skaskiv: 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. Demonstr. Math., 52 (1) (2019), 82-87. doi 10.1515/dema-2019-0008.
A. Bandura, O. Skaskiv: Boundedness of the $L$-index in a direction of entire solutions of second order partial differential equation. Acta Comment. Univ. Tartu. Math., 22 (2) (2018), 223-234. doi 10.12697/ACUTM.2018.22.18.
A.I. Bandura, O.B. Skaskiv: Partial logarithmic derivatives and distribution of zeros of analytic functions in the unit ball of bounded $ L $-index in joint variables. J. Math. Sci. 239 (1) (2019), 17-29. doi 10.1007/s10958-019-04284-z.
A.I. Bandura, O.B. Skaskiv: Exhaustion by balls and entire functions of bounded $ L $-index in joint variables. Ufa Math. J. 11 (1) (2019), 100-113. doi 10.13108/2019-11-1-100.
A. Bandura, O. Skaskiv Analog of Hayman's Theorem and its Application to Some System of Linear Partial Differential Equations. J. Math. Phys., Anal., Geom. 15 (2) (2019), 170-191. doi 10.15407/mag15.02.170.
M.T. Bordulyak: On the growth of entire solutions of linear differential equations. Mat. Stud. 13 (2) (2000), 219-223.
M.T. Bordulyak, M.M. Sheremeta: Boundedness of $l$-index of analytic curves. Mat. Stud. 36 (2) (2011), 152-161.
L.F. Heath: Vector-valued entire functions of bounded index satisfying a differential equation. Journal of Research of NBS 83B (1) (1978), 75-79.
F. Nuray, R.F. Patterson: Vector-valued bivariate entire functions of bounded index satisfying a system of differential equations. Mat. Stud. 49 (1) (2018), 67-74. doi 10.15330/ms.49.1.67-74.
R. Roy, S.M. Shah: Growth properties of vector entire functions satisfying differential equations. Indian J. Math. 28 (1) (1986), 25-35.
R. Roy, S.M. Shah: Vector-valued entire functions satisfying a differential equation. J. Math. Anal. Appl. 116 (2) (1986), 349-362.
M.N. Sheremeta, A.D. Kuzyk: Logarithmic derivative and zeros of an entire function of bounded l-index. Sib. Math. J. 33 (2) (1992), 304-312. doi 10.1007/BF00971102.
M. Sheremeta: Boundedness of $l- M $-index of analytic curves.Visnyk Lviv Un-ty. Ser. Mech.-Math. rm Iss. 75 (2011), 226-231.

Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-index in Joint Variables

Year 2020, Volume: 3 Issue: 1, 9 - 19, 01.03.2020

Vita Baksa Andriy Bandura , Oleh Skaskıv

https://doi.org/10.33205/cma.650977

Cited By: 1

Abstract

Our results concern growth estimates for vector-valued functions of $\mathbb{L}$-index in joint variables which are analytic in the unit ball.

There are deduced analogs of known growth estimates obtained early for functions analytic in the unit ball.

Our estimates contain logarithm of $\sup$-norm instead of logarithm modulus of the function.

They describe the behavior of logarithm of norm of analytic vector-valued function on a skeleton in a bidisc by

behavior of the function $\mathbf{L}.$ These estimates are sharp in a general case.

The presented results are based on bidisc exhaustion of a unit ball.

Keywords

bounded index, bounded $\mathbf{L}$-index in joint variables

References

V.P. Baksa: Analytic vector-functions in the unit ball having bounded $ L $-index in joint variables. Carpathian Math. Publ. 11 (2) (2019), 213-227. doi 10.15330/cmp.11.2.213-227
V.P. Baksa, A.I. Bandura, O.B. Skaskiv: Analogs of Fricke's theorems for analytic vector-valued functions in the unit ball having bounded $ L $-index in joint variables. submitted to Proceedings of IAMM of NASU.
V.P. Baksa, A.I. Bandura, O.B. Skaskiv: Analogs of Hayman's theorem and of logarithmic criterion for analytic vector-valued functions in the unit ball having bounded $ L $-index in joint variables. submitted to Matematica Slovaca.
A. I. Bandura, O. B. Skaskiv: Analytic functions in the unit ball of bounded $ L $-index asymptotic and local properties. Mat. Stud. 48 (1) (2017), 37-73. doi 10.15330/ms.48.1.37-73.
A. Bandura, O. Skaskiv: Sufficient conditions of boundedness of $L$-index and analog of Hayman's Theorem for analytic functions in a ball. Stud. Univ. Babec s-Bolyai Math. 63(4) (2018), 483-501. doi 10.24193/subbmath.2018.4.06.
A. Bandura, O. Skaskiv: Functions analytic in the unit ball having bounded L-index in a direction. Rocky Mountain J. Math. 49 (4) (2019), 1063-1092. doi 10.1216/RMJ-2019-49-4-1063.
A. Bandura, O. Skaskiv: Asymptotic estimates of entire functions of bounded $ L $-index in joint variables. Novi Sad J. Math. 48(1) (2018), 103-116. doi 10.30755/NSJOM.06997.
A. Bandura, N. Petrechko, O. Skaskiv: Maximum modulus in a bidisc of analytic functions of bounded $ L $ -index and an analogue of Hayman's theorem. Matem. Bohem. 143(4) (2018), 339-354. doi 10.21136/MB.2017.0110-16.
A.I. Bandura, O.B. Skaskiv, V.L. Tsvigun: Some characteristic properties of analytic functions in $D\times C$ of bounded $L$-index in joint variables. Bukovyn. Mat. Zh. 6 (1-2) (2018), 21-31. doi 10.31861/bmj2018.01.021.
A.I. Bandura, N.V. Petrechko, O.B. Skaskiv: Analytic in a polydisc functions of bounded $L $ -index in joint variables. Mat. Stud. 46 (1) (2016), 72-80. doi 10.15330/ms.46.1.72-80.
A. Bandura, O. Skaskiv: 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. Demonstr. Math., 52 (1) (2019), 82-87. doi 10.1515/dema-2019-0008.
A. Bandura, O. Skaskiv: Boundedness of the $L$-index in a direction of entire solutions of second order partial differential equation. Acta Comment. Univ. Tartu. Math., 22 (2) (2018), 223-234. doi 10.12697/ACUTM.2018.22.18.
A.I. Bandura, O.B. Skaskiv: Partial logarithmic derivatives and distribution of zeros of analytic functions in the unit ball of bounded $ L $-index in joint variables. J. Math. Sci. 239 (1) (2019), 17-29. doi 10.1007/s10958-019-04284-z.
A.I. Bandura, O.B. Skaskiv: Exhaustion by balls and entire functions of bounded $ L $-index in joint variables. Ufa Math. J. 11 (1) (2019), 100-113. doi 10.13108/2019-11-1-100.
A. Bandura, O. Skaskiv Analog of Hayman's Theorem and its Application to Some System of Linear Partial Differential Equations. J. Math. Phys., Anal., Geom. 15 (2) (2019), 170-191. doi 10.15407/mag15.02.170.
M.T. Bordulyak: On the growth of entire solutions of linear differential equations. Mat. Stud. 13 (2) (2000), 219-223.
M.T. Bordulyak, M.M. Sheremeta: Boundedness of $l$-index of analytic curves. Mat. Stud. 36 (2) (2011), 152-161.
L.F. Heath: Vector-valued entire functions of bounded index satisfying a differential equation. Journal of Research of NBS 83B (1) (1978), 75-79.
F. Nuray, R.F. Patterson: Vector-valued bivariate entire functions of bounded index satisfying a system of differential equations. Mat. Stud. 49 (1) (2018), 67-74. doi 10.15330/ms.49.1.67-74.
R. Roy, S.M. Shah: Growth properties of vector entire functions satisfying differential equations. Indian J. Math. 28 (1) (1986), 25-35.
R. Roy, S.M. Shah: Vector-valued entire functions satisfying a differential equation. J. Math. Anal. Appl. 116 (2) (1986), 349-362.
M.N. Sheremeta, A.D. Kuzyk: Logarithmic derivative and zeros of an entire function of bounded l-index. Sib. Math. J. 33 (2) (1992), 304-312. doi 10.1007/BF00971102.
M. Sheremeta: Boundedness of $l- M $-index of analytic curves.Visnyk Lviv Un-ty. Ser. Mech.-Math. rm Iss. 75 (2011), 226-231.

There are 23 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Articles
Authors	Vita Baksa This is me Andriy Bandura 0000-0003-0598-2237 Oleh Skaskıv This is me 0000-0001-5217-8394
Publication Date	March 1, 2020
Published in Issue	Year 2020 Volume: 3 Issue: 1

Cite

APA	Baksa, V., Bandura, A., & Skaskıv, O. (2020). Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-index in Joint Variables. Constructive Mathematical Analysis, 3(1), 9-19. https://doi.org/10.33205/cma.650977
AMA	Baksa V, Bandura A, Skaskıv O. Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-index in Joint Variables. CMA. March 2020;3(1):9-19. doi:10.33205/cma.650977
Chicago	Baksa, Vita, Andriy Bandura, and Oleh Skaskıv. “Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-Index in Joint Variables”. Constructive Mathematical Analysis 3, no. 1 (March 2020): 9-19. https://doi.org/10.33205/cma.650977.
EndNote	Baksa V, Bandura A, Skaskıv O (March 1, 2020) Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-index in Joint Variables. Constructive Mathematical Analysis 3 1 9–19.
IEEE	V. Baksa, A. Bandura, and O. Skaskıv, “Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-index in Joint Variables”, CMA, vol. 3, no. 1, pp. 9–19, 2020, doi: 10.33205/cma.650977.
ISNAD	Baksa, Vita et al. “Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-Index in Joint Variables”. Constructive Mathematical Analysis 3/1 (March 2020), 9-19. https://doi.org/10.33205/cma.650977.
JAMA	Baksa V, Bandura A, Skaskıv O. Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-index in Joint Variables. CMA. 2020;3:9–19.
MLA	Baksa, Vita et al. “Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-Index in Joint Variables”. Constructive Mathematical Analysis, vol. 3, no. 1, 2020, pp. 9-19, doi:10.33205/cma.650977.
Vancouver	Baksa V, Bandura A, Skaskıv O. Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $\mathbf{L}$-index in Joint Variables. CMA. 2020;3(1):9-19.