Value Distribution Theory And Related Topics

by Barsegian, Grigor A.; Laine, Ilpo; Yang, Chung-Chun

• ISBN13: 9781402079504
• ISBN10: 1402079508
• Format: Hardcover
• Copyright: 2004-05-31
• Publisher: Kluwer Academic Pub

Summary

The volume consists of a collection of articles on the value distribution theory and its applications, both in one and several variables. The applied parts include problems related to geometric function theory, linear operators of entire functions, differential and functional equations, uniqueness and interpolation. A unique feature of the book is an extensive research program by the first editor on the Gamma-lines approach to analysis. Some aspects in the book consider Diophantine type equations for meromorphic functions, offering new challenges to complex analysis. Audience: Researchers and postgraduate students in complex analysis, differential equations and algebraic geometry would find this book of interest.

Table of Contents

Preface	vii
Geometric value distribution theory
Barsegian, G.: A new program of investigations in analysis: Gamma-lines approaches	1	(74)
Sukiasyan, G.: On level sets of quasiconformal mappings	75	(18)
Classical value distribution theory
Alonso, A., Fernández, A. and Pérez, J.: On the unintegrated Nevanlinna fundamental inequality for meromorphic functions of slow growth	93	(12)
Barsegian, G. and Yang, C.-C.: On some new concept of exceptional values	105	(12)
Ciechanowicz, E. and Marchenko, I.: Maximum modulus points, deviations and spreads of meromorphic functions	117	(14)
Craven, T. and Csordas, G.: Composition theorems, multiplier sequences and complex zero decreasing sequences	131	(36)
Korhonen, R.: Nevanlinna theory in an annulus	167	(14)
Marchenko, I. and Nikolenko, I.: On strong asymptotic tracts of functions holomorphic in a disk	181	(8)
Complex differential and functional equations
Barsegian, G., Sarkisian, A. and Yang, C.-C.: A new trend in complex differential equations: quasimeromorphic solutions	189	(12)
Ha, H.K. and Yang, C.-C.: On the functional equation P(f) = Q(g)	201	(8)
He, Y.: Value distribution of the higher order analogues of the first Painlevé equation	209	(10)
Yang, C.-C. and Li, P.: Some further results on the functional equation P(f) = Q(g)	219	(14)
Several variables theory
Aihara, Y.: Recent topics in uniqueness problem for meromorphic mappings	233	(32)
Berenstein, C. and Li, B.Q.: On interpolation problems in Cn	265	(16)
Hu, P.-C. and Yang, C.-C.: Jet bundles and its applications in value distribution of holomorphic mappings	281	(40)
Tu, Z.-H.: Normal families of meromorphic mappings of several complex variables into the complex projective space	321