Abstract
The paper deals with the aspect of the growth of entire functions of several complex variables. The growth of the entire functions with respect to each of the variables separately has been studied by defining partial order and partial type. Finally, we have studied the growth and polynomial approximation of entire function generalized biaxially symmetric potential with respect to each of the variables separately.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Askey, R.: Orthogonal Polynomial and Special Functions. Regional Conference Series in Applied mathematics. SIAM, Philadelphia (1975)
Bose S.K., Sharma D.: Integral functions of two complex variables. Compos. Math. 15, 210–236 (1963)
Gilbert, R.P.: Function Theoretic Methods in Partial Differential Equations. Mathematics in Science and Engineering, vol. 54. Academic Press, New York (1969)
Gilbert, R.P.: Constructive Methods for Elliptic Equations. Lecture Notes in Mathematics, vol. 365. Springer/Academic Press, New York (1974)
Kumar D., Kasana H.S.: Approximation and interpolation of generalized biaxisymmetric potentials. Pan Am. Math. J. 9(1), 55–62 (1999)
Lelong, P., Gruman, L.: Entire Functions of Several Complex variables. A Series of Comprehensive Studies in Mathematics, vol. 282. Springer, Berlin (1986)
McCoy P.A.: Polynomial approximation of generalized biaxisymmetric potentials. J. Approx. Thoery 25, 153–168 (1979)
McCoy P.A.: Extremal properties of generalized biaxially symmetric potentials. Pac. J. Math. 74, 381–389 (1978)
Sato D.: On the rate of growth of entire functions of fast growth. Bull. Am. Math. Soc. 69, 411–414 (1963)
Siciak J.: On some extremal functions and their applications in the theory of analytic functions of several complex variables. Trans. Am. Math. Soc. 105, 322–357 (1962)
Winiarski T.N.: Applications of approximation and interpolation methods to the examination of entire functions of n-complex variables. Ann. Polon. Math. 28, 97–121 (1973)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was done in the memory of Prof. H.S. Kasana, Senior Associate, ICTP, Trieste, Italy.
Rights and permissions
About this article
Cite this article
Kumar, D. Growth and approximation of generalized biaxially symmetric potentials in several complex variables. Ann Univ Ferrara 57, 109–120 (2011). https://doi.org/10.1007/s11565-011-0116-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11565-011-0116-6
Keywords
- Partial order
- Partial type
- Transfinite diameter
- Extremal function
- Hypersurface
- Lagrange interpolation polynomial