Complex Analysis I: Entire and Meromorphic Functions Polyanalytic Functions and Their Generalizations
A.A. Gonchar, Viktor P. Havin, N.K. Nikolski
Springer, 1997 - Mathematics - 261 pages
The works by Weierstrass, Mittag-LefHer and Picard dated back to the seventies of the last century marked the beginning of systematic studies of l the theory of entire and meromorphic functions. The theorems by Weierstrass and Mittag-Leffier gave a general description of the structure of entire and meromorphic functions. The representation of entire functions as an infinite product by Weierstrass served as the basis for studying properties of entire and meromorphic functions. The Picard theorem initiated the theory of value distribution of meromorphic functions. In 1899 Jensen proved a formula which relates the number of zeros of an entire function in a disk with the magnitude of its modulus on the circle. The Jensen formula was of a great importance for the development of the theory of entire and meromorphic functions. The theory of entire functions was shaped as aseparate scientific discipline by Laguerre, Hadamard and Borel in 1882-1900. Borel's book "Legons sur les fonctions entieres" published in 1900 was the first monograph devoted to this theory. The works by R. Nevanlinna during 1920's resulted in the intensive development of the theory of value distribution of meromorphic functions, and were largely responsible for determining its modern character. The fund amen tals of this theory were presented in R. Nevanlinna's book "Le theoreme de Picard-Borel et la theorie des fonctions meromorphes" (1929).
What people are saying - Write a review
We haven't found any reviews in the usual places.