Value Distribution Theory and Related Topics

ISBN-13: 9781402079504 / Angielski / Twarda / 2004 / 333 str.

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

Opis

The Nevanlinna theory of value distribution of meromorphic functions, one of the milestones of complex analysis during the last century, was c- ated to extend the classical results concerning the distribution of of entire functions to the more general setting of meromorphic functions. Later on, a similar reasoning has been applied to algebroid functions, subharmonic functions and meromorphic functions on Riemann surfaces as well as to - alytic functions of several complex variables, holomorphic and meromorphic mappings and to the theory of minimal surfaces. Moreover, several appli- tions of the theory have been exploited, including complex differential and functional equations, complex dynamics and Diophantine equations. The main emphasis of this collection is to direct attention to a number of recently developed novel ideas and generalizations that relate to the - velopment of value distribution theory and its applications. In particular, we mean a recent theory that replaces the conventional consideration of counting within a disc by an analysis of their geometric locations. Another such example is presented by the generalizations of the second main theorem to higher dimensional cases by using the jet theory. Moreover, s- ilar ideas apparently may be applied to several related areas as well, such as to partial differential equations and to differential geometry. Indeed, most of these applications go back to the problem of analyzing zeros of certain complex or real functions, meaning in fact to investigate level sets or level surfaces.

Spis treści

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