Finite or Infinite Dimensional Complex Analysis and Applications

by Son, Le Hung; Tutschke, Wolfgang; Yang, Chung-Chun

• ISBN13: 9781402076589
• ISBN10: 1402076584
• Format: Hardcover
• Copyright: 2003-11-01
• Publisher: Springer Verlag

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.

Table of Contents

Preface	ix
I. PLENARY TALKS AND SURVEYS
1 Nevanlinna theory and Diophantine approximations	1	(20)
Pei- Chu Hu, Chung- Chun Yang
2 In Ramanujan's Shadow	21	(14)
Irwin Kra
3 Holomorphic functions on the Lie ball and related topics	35	(10)
Mitsuo Morimoto, Keiko Fujita
4 Invariance of Plurigenera and Torsion-Freeness of Direct Image Sheaves of Pluricanonial Bundles	45	(40)
Yum-Tong Siu
5 Maxwell's equations in Clifford calculus framework - an overview on the development	85	(16)
Wolfgang Spröflig
6 Generalized Analytic Functions and their contributions to the development of Mathematical Analysis	101	(16)
W. Tutschke
II. COMPLEX METHODS IN THE PLANE
7 On qp sequences	117	(10)
Rauno Aulaskari, Shamil Makhmutov, Hasi Wulan
8 Reconstruction of an Analytic Function from a Sequence of Values: Existence and Regularization	127	(16)
Dang Djnh Ang, Vy Khoi Le, Dang Duc Trong
9 p-adic Interpolation and Applications	143	(10)
Ha Huy Khoai, Le Thi Hoai Thu
10 Refined Order and the Patey Problem in Vector Spaces	153	(16)
Chuan-Gan Hu, Chao Liu
11 Integral representation of p-adic functions	169	(12)
Le Thi Hoai Thu
12 Malmquist-Yosida type theorems for algebraic differential equations	181	(12)
Liangwen Liao, Chung-Chun Yang
13 Transformation techniques for partial differential equations	193	(14)
Jürgen Pungel
14 Besov-type Characterizations for Quaternionic Bloch Functions	207	(14)
L.F. Reséndis O., L.M. Tovar S.
15 Bergman and Bauer Operators for Elliptic Equations in two Independent Variables	221	(24)
K.W. Tomantschger
16 Some results on QK-type spaces	245	(10)
Hasj Wulan
III. ANALYSIS IN HIGHER DIMENSIONS
17 Representations in Polydomains	255	(14)
H. Begehr
18 On Bq spaces of hyperholomorphic functions and the Bloch space in R3	269	(18)
K. Gürlebeck, A. El-Sayed Ahmed
19 Regeneration in complex, quaternion and Clifford analysis	287	(12)
Joji Kajiwara, Xiao Dong Li, Kwang Ho Shon
20 A note on sesquilinear forms and the generalized uncertainty relations in *-algebras	299	(10)
Ken Kuriyama, Shigeru Furuichi, Kenjiro Yanagi
21 The Hartogs Extension Theorem for the Multi-regular functions Taking Values in a Clifford algebra	309	(14)
Le Hung Son, Nguyen Thanh Van
22 The extension of entire functions of nuclear type on locally convex spaces	323	(8)
Masaru Nishihara
23 Some Properties of the Inhomogeneous Generalized Cauchy-Riemann Systems in Quaternionic Algebra and its Applications	331	(14)
Nguyen Thanh Van
24 The Fundamental Solution of the Hyperbolic Dirac-Equation	345	(16)
D. Eelbode, F. Sommen
25 Inhomogeneous ordinary differential equations and local cohomologies and residues	361	(10)
S. Tajima
26 Infinite dimensional CR category	371
Shigeru Takeuchi