Asymptotic Characteristics of Entire Functions and Their Applications in Mathematics and Biophysics

Asymptotic Characteristics of Entire Functions and Their Applications in Mathematics and Biophysics is the second edition of the same book in Russian, revised and enlarged. It is devoted to asymptotical questions of the theory of entire and plurisubharmonic functions. The new and traditional asymptotical characteristics of entire functions of one and many variables are studied. Applications of these indices in different fields of complex analysis are considered, for example Borel-Laplace transformations and their modifications, Mittag-Leffler function and its natural generalizations, integral methods of summation of power series and Riemann surfaces.

In the second edition, a new appendix is devoted to the consideration of those questions for a class of entire functions of proximate order. A separate chapter is devoted to applications in biophysics, where the algorithms of mathematical analysis of homeostasis system behaviour, dynamics under external influence are investigated, which may be used in different fields of natural science and technique.

This book is of interest to research specialists in theoretical and applied mathematics, postgraduates and students of universities who are interested in complex and real analysis and its applications.

Inhalt
1 Preliminary.- 2 A Method of Identifying Homeostasis Relaxation Characteristics.- 3 Indicator Diagram of an Entire Function of One Variable with Nonnegative Indicator.- 4 Plane Indicator Diagram of Entire Function of Order ? > 0 with the Indicator of General Form.- 5 Spaces of Entire Functions of Order ? > 0 with Restrictions on the indicator.- 6 Geometrical Analysis of Asymptotics of Functions Plurisubgarmonic in ?n.- 7 Growth Characteristics of Entire Functions (Orders, Types) and Their Applications.- 8 Indicator Diagram of an Entire Function of Several Variables with Nonnegative Indicator.- Appendix A Riemann Surface of the Inverse Function for a Polynomial of Fractional Order.- A.1 Some topological information.- A.2 Construction of the Riemann surface in question and its properties.- Appendix B Indicator and Conjugate Diagrams of Entire Function of a Given Proximate Order.- B.1 Necessary information about proximate orders. Indicator diagram.- B.2 Analytic proximate orders and associated functions.- B.3 Entire functions associated with an analytic proximate order.- B.4 Entire function of a given proximate order and with nonnegative indicator.- B.5 Analytic proximate orders generated by entire or meromorphic functions.- B.6 Applications of the preceding results.- Comments.- References to Chapters 1, 38.- References to Chapter 2.- Notation.