Complex analysis and applications : proceedings of the 13th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Shantou University, China, 8-12 August 2005

This valuable collection of articles presents the latest methods and results in complex analysis and its applications. The present trends in complex analysis reflected in the book are concentrated in the following research directions: Clifford analysis, complex dynamical systems, complex function spaces, complex numerical analysis, qusiconformal mapping, Riemann surfaces, Teichmuller theory and Klainian groups, several complex variables, and value distribution theory. CONTENTS......Page 8 Preface......Page 6 1. Introduction......Page 12 2. The Dirichlet problem......Page 13 3. The Neumann problem......Page 16 References......Page 21 1. Introduction......Page 22 2. The real matrix representation of elements in Cl0,3......Page 23 3. The Moore-Penrose inverse of elements in Cl0,3 ......Page 26 4. Linear equation ax = xb over Cl0,3......Page 27 References......Page 32 A Change of Scale Formula for Wiener Integrals of Unbounded Functions over Wiener Paths in Abstract Wiener Space......Page 33 1. Introduction and preliminaries......Page 34 2. Wiener paths in abstract Wiener space......Page 36 3. A change of scale formula over Wiener paths in abstract Wiener space......Page 37 4. A change of scale formula on abstract Wiener space......Page 48 References......Page 53 1. Introduction and Preliminaries......Page 55 2. Lemmas for Proof of Main Results......Page 58 3. Main Results......Page 60 References......Page 62 1. Introduction......Page 64 2. Bounded symmetric domains......Page 67 3. Invariant differential operators......Page 69 4. Bergman spaces and kernels......Page 70 5. Peter-Weyl decomposition......Page 71 6. Bloch spaces and Qv spaces on bounded symmetric domains......Page 72 8. Composition series......Page 74 9. Results......Page 76 10. Sketches of proofs......Page 78 11. Open problems......Page 81 References......Page 82 1. Introduction......Page 83 2. Short proof of Theorem 1.1......Page 84 References......Page 87 1. Problem "1CM+3IM=4CM" and Gundersen's Question......Page 89 2. Some Auxiliary Functions......Page 90 3. A Branch of √φ and its Characteristic Function......Page 91 4. The Power Expansions of σ at Zeros, 1-Points, and c-Points of f......Page 93 5. Jensen's Formula for F(σ)......Page 95 6. Some Results on the Uniqueness of Meromorphic Functions that Share Four values......Page 96 References......Page 98 1. Introduction......Page 100 2. Main results......Page 101 3. Preliminaries for the proofs of the main results......Page 102 4. Proof of Theorem 1......Page 106 5. Proof of Theorem 2......Page 110 References......Page 111 1. Introduction......Page 112 2. Construction of a certain holomorphic family (M,π,R) of Riemann surfaces......Page 114 3. Defining equations for (M,π,R)......Page 115 5. Injectivity of the moduli map J of (M,π,R)......Page 117 References......Page 119 α-Asymptotically Conformal Fixed Points and Holomorphic Motions......Page 120 1. Introduction......Page 121 2. Holomorphic Motions and Quasiconformal Maps......Page 122 3. α-Asymptotically conformal fixed points......Page 125 4. Linearization for α-asymptotically conformal attracting or repelling fixed points......Page 127 5. Normal forms for α-asymptotically conformal super-attracting fixed points......Page 132 References......Page 139 The Hyper-Order of Solutions of Certain High Order Differential Equations......Page 141 1. Lemmas......Page 143 2. Proof of Theorem 1......Page 145 References......Page 147 1. Introduction and results......Page 148 2. Some lemmas......Page 152 3. Proof of Theorem 1......Page 153 References......Page 158 1. Introduction......Page 160 2. Preliminaries......Page 161 3. The Proof of the Main Theorem......Page 163 References......Page 169 1. Introduction and Main Results......Page 170 2. Some Lemmas......Page 173 3. Proofs of Main Theorems......Page 176 References......Page 179 1. Introduction and Main Results......Page 180 2. Some Lemmas......Page 182 3. Proof of Theorems......Page 185 References......Page 188 1. Introduction......Page 189 2. Main Results......Page 190 References......Page 195 1. Introduction......Page 196 2. Theorem and its Proof......Page 197 References......Page 199 1. Introduction......Page 200 2. Transversal Maps......Page 201 4. Examples......Page 204 References......Page 206 1. Introduction......Page 208 2. The coefficients of logB(α,β) functions......Page 209 3. logB(α,β) space and Cesàro means......Page 211 References......Page 213 1. Takebe Katahiro......Page 214 2. Takebe's Infinite Series Expansion......Page 215 3. Squared Half Back Arc and Sagitta......Page 216 4. Numerical Method to Find the Infinite Series Expansion......Page 217 5. Approximation Formulas by Interpolation......Page 218 6. Algebraic Method to Find the Infinite Series Expansion......Page 220 7. Counting Board Algebra and Generalized Division......Page 221 8. The Taylor Expansion Formula in Japanese Mathematics......Page 223 9. Taking the Limit......Page 226 References......Page 228 1. Introduction and Main Results......Page 229 2. Some Lemmas......Page 230 3. Proof of Theorem......Page 231 References......Page 235 1. Introduction......Page 236 2. The boundedness and compactness of IΦ on Bα......Page 237 3. The boundedness of JΦ and IΦ on BMOAα......Page 239 References......Page 241 1. Introduction......Page 242 2. Main Results......Page 244 References......Page 252 1. Introduction and results......Page 253 2. Lemmas......Page 255 3. Proof of theorem......Page 258 References......Page 259 1. Introduction......Page 260 2. Preliminaries......Page 261 3. Main Results......Page 263 References......Page 271 1. Introduction......Page 272 2. Fredholm Module......Page 273 3. Predholm Module of Cauchy Integral Operators......Page 275 References......Page 277 1. Introduction......Page 278 2. Preliminaries and lemmas......Page 279 3. The concepts of ψ-modulus and ψ-capacities and Theorem 1......Page 281 4. Main theorems and their proofs......Page 283 References......Page 286 A Criterion of Bloch Functions and Little Bloch Functions......Page 287 References......Page 291 Some Results of Uniqueness for Algebroid Functions......Page 292 References......Page 303 1. Introduction......Page 304 2. Delta inequalities......Page 306 3. Proof of Theorem 1......Page 307 4. Proof of Theorem 2......Page 309 References......Page 310 1. Introduction and Main Result......Page 311 2. Some Lemmas and Notations......Page 313 3. Proof of Theorem 1......Page 316 References......Page 319 1. Introduction......Page 320 2. Some lemmas......Page 321 3. The main theorems......Page 322 References......Page 329 1. Main Results......Page 331 2. Some Lemmas......Page 332 3. Proof of Theorem 1......Page 337 References......Page 338 1. Introduction......Page 339 2. The automorphism group......Page 341 3. Möbius invariance of Bp......Page 343 References......Page 348 This valuable collection of articles presents the latest methods and results in complex analysis and its applications. The present trends in complex analysis reflected in the book are concentrated in the following research directions: Clifford analysis, complex dynamical systems, complex function spaces, complex numerical analysis, qusiconformal mapping, Riemann surfaces, Teichmüller theory and Klainian groups, several complex variables, and value distribution theory. Presents the methods and results in complex analysis and its applications. This book also reflects on the trends in complex analysis, which are concentrated in the research directions of Clifford analysis, complex dynamical systems, complex function spaces, complex numerical analysis, qusiconformal mapping, Riemann surfaces, and other areas.