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Asymptotic Characteristics of Entire Functions and Their Applications in Mathematics and Biophysics Second Edition 2003 [Kõva köide]

  • Formaat: Hardback, 362 pages, kõrgus x laius: 235x155 mm, kaal: 813 g, XXIV, 362 p., 1 Hardback
  • Sari: Mathematics and Its Applications 559
  • Ilmumisaeg: 31-Aug-2003
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1402014627
  • ISBN-13: 9781402014628
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Asymptotic Characteristics of Entire Functions and Their Applications in Mathematics and Biophysics Second Edition 2003Suurem pilt
  • Formaat: Hardback, 362 pages, kõrgus x laius: 235x155 mm, kaal: 813 g, XXIV, 362 p., 1 Hardback
  • Sari: Mathematics and Its Applications 559
  • Ilmumisaeg: 31-Aug-2003
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1402014627
  • ISBN-13: 9781402014628
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781402014628.html
Märksõnad:
For specialists in theoretical and applied mathematics and mathematical biophysics, and graduate and undergraduate students in those fields, Maergoiz (computational modelling, Krasnoyarsk State Academy of Architecture and Civil Engineering, Russia describes traditional and new asymptotic characteristics of entire functions of one or several complex variables. He also explains and demonstrates how to apply the characteristics in various areas of complex analysis, including Mittag-Leffler functions and their natural generalizations, integral methods of summing the power series, and Riemann surfaces. No mention is made of an earlier English edition, but of a second edition of a Russian 1991 publication. Annotation (c) Book News, Inc., Portland, OR (booknews.com)

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.

This revised and enlarged second edition is devoted to asymptotical questions of the theory of entire and plurisubharmonic functions. A separate chapter deals with applications in biophysics. The book is of interest to research specialists in theoretical and applied mathematics, postgraduates and students who are interested in complex and real analysis and its applications.
From the Editors of Russian Edition xiii
Foreword to the Russian Edition xv
Introduction xxi
Chapter 1 Preliminary 1(50)
1.1 On the growth of nondecreasing functions of one variable
1(1)
1.2 Semicontinuous functions
2(2)
1.3 Convex sets and associated functions
4(5)
1.4 Convex functions
9(5)
1.5 Duality of convex functions
14(5)
1.6 Asymptotic properties of convex functions
19(2)
1.7 Minkowski theorem on convex bodies
21(1)
1.8 Plurisubharmonic functions
22(4)
1.9 Trigonometrically p-convex functions
26(15)
1.10 Selected facts about entire functions of one variable
41(10)
Chapter 2 A Method of Identifying Homeostasis Relaxation Characteristics 51(33)
2.1 Homeostasis system relaxation characteristics and the problem of their identification
51(2)
2.2 Algorithm of recovering a quasipolinomial by its moments
53(11)
2.3 Algorithm of approximation of discrete functions by quasipolinomials (identification algorithm)
64(5)
2.4 The case of quasipolynomials of order 2 and 3
69(7)
2.5 The case of wave-type homeostasis processes
76(8)
Chapter 3 Indicator Diagram of an Entire Function of One Variable with Nonnegative Indicator 84(18)
3.1 Plane p-convex sets and the indicator diagram
85(7)
3.2 Analog of the Polya theorem for an entire function of order p not equal to 1 and with nonnegative indicator
92(4)
3.3 The generalized Borel polygon of a power series
96(6)
Chapter 4 Plane Indicator Diagram of Entire Function of Order p greater than 0 with the Indicator of General Form 102(69)
4.1 Minimal trigonometrically p-convex functions
103(12)
4.2 Many-sheeted diagrams associated with the functions of class PP
115(24)
4.3 The relationship of the polynomials a(z)=zP + a1zP-1 + ... + anzP-n with functions of class MP
139(12)
4.4 Plane (p, α)-convex sets and the plane indicator diagram of an entire function of order p greater than 0
151(20)
Chapter 5 Spaces of Entire Functions of Order p greater than 0 with Restrictions on the indicator 171(23)
5.1 Entire function of two variables associated with a polynomial in Bp,(1)
172(8)
5.2 The analog of Boref's transformation and realization of the spaces [ p,h(θ)), [ p,h(θ)]
180(5)
5.3 Applications of the analog of the Polya theorem
185(9)
Chapter 6 Geometrical Analysis of Asymptotics of Functions Plurisubgarmonic in Cn 194(26)
6.1 Simplest properties of functions of classes B, U
194(2)
6.2 Various definitions of orders of functions of class U
196(8)
6.3 Local Αφ-type structure for function in U
204(11)
6.4 Global Αφ-type structure for function P in U
215(5)
Chapter 7 Growth Characteristics of Entire Functions (Orders, Types) and Their Applications 220(21)
7.1 Relationship between the growth characteristics of an entire function and its Taylor coefficients
221(3)
7.2 Existence of entire functions with prescribed growth characteristics
224(8)
7.3 The modulus maximum and the maximal term of an entire function: comparative growth
232(5)
7.4 On the growth of the Nevanlinna characteristic for an entire function of several variables
237(4)
Chapter 8 Indicator Diagram of an Entire Function of Several Variables with Nonnegative Indicator 241(21)
8.1 System of indicators and indicator diagrams of an entire function of several variables
242(2)
8.2 Circular sets and their properties
244(11)
8.3 An analog of the Polya-Martineau-Ehrenpreis Theorem
255(4)
8.4 Consequences from Theorem 8.3.1
259(3)
Appendix A Riemann Surface of the Inverse Function for a Polynomial of Fractional Order 262(24)
A.1 Some topological information
263(5)
A.2 Construction of the Riemann surface in question and its properties
268(18)
Appendix B Indicator and Conjugate Diagrams of Entire Function of a Given Proximate Order 286(48)
B.1 Necessary information about proximate orders. Indicator diagram
286(4)
B.2 Analytic proximate orders and associated functions
290(13)
B.3 Entire functions associated with an analytic proximate order
303(12)
B.4 Entire function of a given proximate order and with nonnegative indicator
315(5)
B.5 Analytic proximate orders generated by entire or meromorphic functions
320(7)
B.6 Applications of the preceding results
327(7)
Comments 334(14)
Bibliography 348(13)
References to
Chapters 1, 3-8
348(10)
References to
Chapter 2
358(3)
Notation 361