Maximum modulus in a bidisc of analytic functions of bounded 𝐋 -index and an analogue of Hayman’s theorem

Andriy Bandura; Nataliia Petrechko; Oleh Skaskiv

Mathematica Bohemica (2018)

  • Volume: 143, Issue: 4, page 339-354
  • ISSN: 0862-7959

Abstract

top
We generalize some criteria of boundedness of 𝐋 -index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of ( p + 1 ) th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).

How to cite

top

Bandura, Andriy, Petrechko, Nataliia, and Skaskiv, Oleh. "Maximum modulus in a bidisc of analytic functions of bounded ${\bf L}$-index and an analogue of Hayman’s theorem." Mathematica Bohemica 143.4 (2018): 339-354. <http://eudml.org/doc/294506>.

@article{Bandura2018,
abstract = {We generalize some criteria of boundedness of $\mathbf \{L\}$-index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of $(p+1)$th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).},
author = {Bandura, Andriy, Petrechko, Nataliia, Skaskiv, Oleh},
journal = {Mathematica Bohemica},
keywords = {analytic function; bidisc; bounded $\{\mathbf \{L\}\}$-index in joint variables; maximum modulus; partial derivative; Cauchy’s integral formula},
language = {eng},
number = {4},
pages = {339-354},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Maximum modulus in a bidisc of analytic functions of bounded $\{\bf L\}$-index and an analogue of Hayman’s theorem},
url = {http://eudml.org/doc/294506},
volume = {143},
year = {2018},
}

TY - JOUR
AU - Bandura, Andriy
AU - Petrechko, Nataliia
AU - Skaskiv, Oleh
TI - Maximum modulus in a bidisc of analytic functions of bounded ${\bf L}$-index and an analogue of Hayman’s theorem
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 4
SP - 339
EP - 354
AB - We generalize some criteria of boundedness of $\mathbf {L}$-index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of $(p+1)$th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).
LA - eng
KW - analytic function; bidisc; bounded ${\mathbf {L}}$-index in joint variables; maximum modulus; partial derivative; Cauchy’s integral formula
UR - http://eudml.org/doc/294506
ER -

References

top
  1. Bandura, A., New criteria of boundedness of L-index in joint variables for entire functions, Mat. Visn. Nauk. Tov. Im. Shevchenka 13 (2016), 58-67 Ukrainian. (2016) Zbl06742099
  2. Bandura, A. I., Bordulyak, M. T., Skaskiv, O. B., 10.15330/ms.45.1.12-26, Mat. Stud. 45 (2016), 12-26. (2016) Zbl1353.30030MR3561322DOI10.15330/ms.45.1.12-26
  3. Bandura, A. I., Skaskiv, O. B., Entire Functions of Several Variables of Bounded Index, Chyslo, Lviv (2015). (2015) Zbl1342.32001
  4. Bandura, A. I., Skaskiv, O. B., Analytic in the unit ball functions of bounded L -index in direction, Avaible at https://arxiv.org/abs/1501.04166. MR3702166
  5. Bandura, A. I., Petrechko, N. V., Skaskiv, O. B., 10.15330/ms.46.1.72-80, Mat. Stud. 46 (2016), 72-80. (2016) Zbl1373.30043MR3649050DOI10.15330/ms.46.1.72-80
  6. Bordulyak, M. T., The space of entire functions in n of bounded L -index, Mat. Stud. 4 (1995), 53-58. (1995) Zbl1023.32500MR1692641
  7. Bordulyak, M. T., Sheremeta, M. M., Boundedness of the L -index of an entire function of several variables, Dopov./Dokl. Akad. Nauk Ukraï ni 9 (1993), 10-13 Ukrainian. (1993) MR1300779
  8. Krishna, J. Gopala, Shah, S. M., Functions of bounded indices in one and several complex variables, Math. Essays dedicated to A. J. Macintyre Ohio Univ. Press, Athens, Ohio (1970), 223-235. (1970) Zbl0205.09302MR0271345
  9. Hayman, W. K., 10.2140/pjm.1973.44.117, Pac. J. Math. 44 (1973), 117-137. (1973) Zbl0248.30026MR0316693DOI10.2140/pjm.1973.44.117
  10. Kushnir, V. O., Sheremeta, M. M., Analytic functions of bounded l -index, Mat. Stud. 12 (1999), 59-66. (1999) Zbl0948.30031MR1737831
  11. Lepson, B., Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index, Entire Funct. and Relat. Parts of Anal., La Jolla, Calif. 1966 Proc. Sympos. Pure Math. 11, AMS, Providence, Rhode Island (1968), 298-307. (1968) Zbl0199.12902MR0237788
  12. Nuray, F., Patterson, R. F., 10.4418/2015.70.2.14, Matematiche 70 (2015), 225-233. (2015) Zbl1342.32006MR3437188DOI10.4418/2015.70.2.14
  13. Salmassi, M., Functions of bounded indices in several variables, Indian J. Math. 31 (1989), 249-257. (1989) Zbl0699.32004MR1042643
  14. Sheremeta, M., Analytic Functions of Bounded Index, Mathematical Studies Monograph Series 6. VNTL Publishers, Lviv (1999). (1999) Zbl0980.30020MR1751042
  15. Strochyk, S. N., Sheremeta, M. M., Analytic in the unit disc functions of bounded index, Dopov./Dokl. Akad. Nauk Ukraï ni 1 (1993), 19-22 Ukrainian. (1993) Zbl0783.30025MR1222997

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.