Approximation of entire functions of slow growth on compact sets

G. S. Srivastava; Susheel Kumar

Archivum Mathematicum (2009)

  • Volume: 045, Issue: 2, page 137-146
  • ISSN: 0044-8753

Abstract

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In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth have been obtained in terms of approximation and interpolation errors.

How to cite

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Srivastava, G. S., and Kumar, Susheel. "Approximation of entire functions of slow growth on compact sets." Archivum Mathematicum 045.2 (2009): 137-146. <http://eudml.org/doc/250679>.

@article{Srivastava2009,
abstract = {In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth have been obtained in terms of approximation and interpolation errors.},
author = {Srivastava, G. S., Kumar, Susheel},
journal = {Archivum Mathematicum},
keywords = {entire function; Siciak extremal function; generalized order; generalized type; approximation errors; interpolation errors; entire function; Siciak extremal function; generalized order; generalized type; approximation error; interpolation error},
language = {eng},
number = {2},
pages = {137-146},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Approximation of entire functions of slow growth on compact sets},
url = {http://eudml.org/doc/250679},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Srivastava, G. S.
AU - Kumar, Susheel
TI - Approximation of entire functions of slow growth on compact sets
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 2
SP - 137
EP - 146
AB - In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth have been obtained in terms of approximation and interpolation errors.
LA - eng
KW - entire function; Siciak extremal function; generalized order; generalized type; approximation errors; interpolation errors; entire function; Siciak extremal function; generalized order; generalized type; approximation error; interpolation error
UR - http://eudml.org/doc/250679
ER -

References

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  1. Ganti, R., Srivastava, G. S., Approximation of entire functions of slow growth, General Math. 14 (2) (2006), 65–82. (2006) Zbl1164.30301MR2270298
  2. Janik, A., A characterization of the growth of analytic functions by means of polynomial approximation, Univ. Iagel. Acta Math. 24 (1984), 295–319. (1984) Zbl0554.32015MR0815914
  3. Janik, A., On approximation of entire functions and generalized order, Univ. Iagel. Acta Math. 24 (1984), 321–326. (1984) MR0815915
  4. Kapoor, G. P., Nautiyal, A., 10.1016/0021-9045(81)90022-8, J. Approx. Theory 32 (1981), 64–75. (1981) Zbl0495.41005MR0629582DOI10.1016/0021-9045(81)90022-8
  5. Seremeta, M. N., On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion, Amer. Math. Soc. Transl. Ser. 2 88 (1970), 291–301. (1970) 
  6. Shah, S. M., 10.1016/0021-9045(77)90095-8, J. Approx. Theory 19 (1977), 315–324. (1977) MR0440254DOI10.1016/0021-9045(77)90095-8
  7. Winiarski, T., Application of approximation and interpolation methods to the examination of entire functions of n complex variables, Ann. Polon. Math. 28 (1973), 97–121. (1973) Zbl0257.32008MR0328091

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