Finite or infinite dimensional complex analysis and applications / edited by Le Hung Son, W. Tutschke, C.C. Yang.

Format:

Book

Contributor:

Son, Le Hung.

Tutschke, Wolfgang

Yang, Chung-Chun, 1942-

Rosengarten Family Fund.

Language:

English

Subjects (All):

Functions of complex variables.

Analytic functions.

Clifford algebras.

Value distribution theory.

Mathematical analysis.

Physical Description:

xi, 381 pages ; 25 cm

Place of Publication:

Boston : Kluwer Academic, [2004]

Summary:

There is almost no field in mathematics that does not use mathematical analysis. Computer methods in applied mathematics are often based on statements and procedures of mathematical analysis as well. An important part of mathematical analysis is complex analysis because it has many applications in various branches of math. Present trends in complex analysis, which are reflected in the book, are mainly concentrated on the following four research directions: -Value distribution theory and its applications, -Holomorphic functions in several (finitely or infinitely many) complex variables, -Clifford analysis, I.e., complex methods in higher-dimensional real Euclidian spaces, -Generalized analytic functions. A specific feature of today's complex analysis is combining methods of Clifford analysis. This leads to a theory of multi-regular functions.

Contents:

I. Plenary Talks and Surveys

1 Nevanlinna theory and Diophantine approximations / Pei-Chu Hu, Chung-Chun Yang 1

2 In Ramanujan's Shadow / Irwin Kra 21

3 Holomorphic functions on the Lie ball and related topics / Mitsuo Morimoto, Keiko Fujita 35

4 Invariance of Plurigenera and Torsion-Freeness of Direct Image Sheaves of Pluricanonial Bundles / Yum-Tong Siu 45

5 Maxwell's equations in Clifford calculus framework

an overview on the development / Wolfgang Sprossig 85

6 Generalized Analytic Functions and their contributions to the development of Mathematical Analysis / W. Tutschke 101

II. Complex Methods in the Plane

7 On q[subscript p] sequences / Rauno Aulaskari, Shamil Makhmutov, Hasi Wulan 117

8 Reconstruction of an Analytic Function from a Sequence of Values: Existence and Regularization / Dang Dinh Ang, Vy Khoi Le, Dang Duc Trong 127

9 p-adic Interpolation and Applications / Ha Huy Khoai, Le Thi Hoai Thu 143

10 Refined Order and the Paley Problem in Vector Spaces / Chuan-Gan Hu, Chao Liu 153

11 Integral representation of p-adic functions / Le Thi Hoai Thu 169

12 Malmquist-Yosida type theorems for algebraic differential equations / Liangwen Liao, Chung-Chun Yang 181

13 Transformation techniques for partial differential equations / Jurgen Pungel 193

14 Besov-type Characterizations for Quaternionic Bloch Functions / L. F. Resendis O., L. M. Tovar S. 207

15 Bergman and Bauer Operators for Elliptic Equations in two Independent Variables / K.W. Tomantschger 221

16 Some results on Q[subscript K]-type spaces / Hasi Wulan 245

III. Analysis in Higher Dimensions

17 Representations in Polydomains / H. Begehr 255

18 On B[superscript q] spaces of hyperholomorphic functions and the Bloch space in R[superscript 3] / K. Gurlebeck, A. El-Sayed Ahmed 269

19 Regeneration in complex, quaternion and Clifford analysis / Joji Kajiwara, Xiao Dong Li, Kwang Ho Shon 287

20 A note on sesquilinear forms and the generalized uncertainty relations in *-algebras / Ken Kuriyama, Shigeru Furuichi, Kenjiro Yanagi 299

21 The Hartogs Extension Theorem for the Multi-regular functions Taking Values in a Clifford algebra / Le Hung Son, Nguyen Thanh Van 309

22 The extension of entire functions of nuclear type on locally convex spaces / Masaru Nishihara 323

23 Some Properties of the Inhomogeneous Generalized Cauchy-Riemann Systems in Quaternionic Algebra and its Applications / Nguyen Thanh Van 331

24 The Fundamental Solution of the Hyperbolic Dirac-Equation / D. Eelbode, F. Sommen 345

25 Inhomogeneous ordinary differential equations and local cohomologies and residues / S. Tajima 361

26 Infinite dimensional CR category / Shigeru Takeuchi 371.

Notes:

Includes bibliographical references.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

1402076584

OCLC:

53099090