Advances in Analysis

by Begehr, Heinrich G. W.; Gilbert, Robert P.; Muldoon, E.; Wong, Man Wah

• ISBN13: 9789812563989
• ISBN10: 9812563989
• Format: Hardcover
• Copyright: 2005-07-30
• Publisher: World Scientific Pub Co Inc

Summary

This authoritative volume comprises the plenary lectures and articles by many of the field's leading researchers who were brought together for the fourth time at the congress of the International Society for Analysis, its Applications and Computation (ISAAC). A wide spectrum of topics in modern analysis is covered by the fully refereed contributions, such as complex analysis, nonlinear analysis, inverse problems, wavelets, signals and images. In particular, important areas--"not given special emphasis in previous meetings--"include special functions and orthogonal polynomials, harmonic analysis, and partial differential equations.

Table of Contents

Preface	p. v
Lee Lorch: Honorary Life Membership in ISAAC	p. vii
Contents	p. ix
Plenary Lectures
Evaluation of Sylvester Type Determinants using Orthogonal Polynomials	p. 1
Geometric Analysis on SubRiemannian Manifolds	p. 17
A Survey of Hardy Type Theorems	p. 39
Approximation Theory
Optimal sk-Spline Approximation of Sobolev's Classes on the 2-Sphere	p. 71
sk-Spline Approximation on the Torus	p. 81
Entropy Numbers of Sobolev and Besov Classes on Homogeneous Spaces	p. 89
Operator Equations and Best Approximation Problems in Reproducing Kernel Hilbert Spaces with Tikhonov Regularization	p. 99
Banach Spaces of Analytic Functions
Finite Fourier Transforms and the Zeros of the Riemann [xi]-Function	p. 109
B[superscript p], Q[subscript p] Spaces and Harmonic Majorants	p. 121
The (t, [alpha])-Lattice and Decomposition Theory for Function Spaces	p. 139
Boundary Value Problems and Integral Equations
On a Generalization of the N. A. Davydov Theorem	p. 159
Dual Integral Equations Method for Some Mixed Boundary Value Problems	p. 167
One Parameter-Dependent Nonlinear Elliptic Boundary Value Problems Arising in Population Dynamics	p. 177
Complex and Functional Analytic Methods in Partial Differential Equations
Combined Integral Representations	p. 187
Remarks on Quantum Differential Operators	p. 197
The Inverse Monodromy Problem in a Class of Knizhnik-Zamolodchikov Equations	p. 211
Reduction of Two Dimensional Neumann and Mixed Boundary Value Problems to Dirichlet Boundary Value Problems	p. 221
Lipschitz Type Inequalities for a Domain Dependent Neumann Eigenvalue Problem for the Laplace Operator	p. 227
Half Robin Problems for the Dirac Operator in the Unit Ball of R[superscript m] (m [greater than or equal] 3)	p. 235
Harmonic Analysis and Partial Differential Equations
Problems Related to the Analytic Representation of Tempered Distributions	p. 245
Strong Unique Continuation for Generalized Baouendi-Grushin Operators	p. 255
Schoenberg's Theorem for Positive Definite Functions on Heisenberg Groups	p. 265
Weak and Strong Solutions for Pseudo-Differential Operators	p. 275
Hemivariational Inequalities and Applications
Comparison Results for Quasilinear Elliptic Hemivariational Inequalities	p. 285
Hemivariational Inequalities Modeling Dynamic Viscoelastic Contact Problems with Friction	p. 295
Sensitivity Analysis for Generalized Variational and Hemivariational Inequalities	p. 305
Hyperbolic Problems: Degeneracies, Nonlinearities and Global Existence
A Smoothing Property of Schrodinger Equations and a Global Existence Result for Derivative Nonlinear Equations	p. 315
Existence and Blow up for a Wave Equation with a Cubic Convolution	p. 321
Zeros and Signs of Solutions for Some Reaction-Diffusion Systems	p. 327
Inverse Problems
Constructions of Approximate Solutions for Linear Differential Equations by Reproducing Kernels and Inverse Problems	p. 335
Ultrasound as a Diagnostic Tool to Determine Osteoporosis	p. 345
Remarks on Quantum KdV	p. 355
A Mathematical Model of Ductal Carcinoma in Situ and Its Characteristic Patterns	p. 365
Nonlinear Analysis and Applications
Classical Dynamics of Quantum Variations	p. 375
Orthogonal Polynomials and Special Functions
On the Zeros of a Transcendental Function	p. 385
Evaluation of Sylvester Type Determinants Using Block-Triangularization	p. 395
Square Summability with Geometric Weight for Classical Orthogonal Expansions	p. 407
The First Positive Zeros of Cylinder Functions and of Their Derivatives	p. 423
Reproducing Kernels and Related Topics
Bergman Kernel for Complex Harmonic Functions on Some Balls	p. 429
Applications of Reproducing Kernels to Best Appoximations, Tikhonov Regularizations and Inverse Problems	p. 439
Equality Conditions for General Norm Inequalities in Reproducing Kernel Hilbert Spaces	p. 447
Time-Frequency Analysis, Wavelets and Applications
Comparing Multiresolution SVD with Other Methods for Image Compression	p. 457
Non-Translation-Invariance in Principal Shift-Invariant Spaces	p. 471
Time-Frequency Spectra of Music	p. 487
Toeplitz-Like Structures in Analysis and Applied Sciences
Dynamics of Spectra of Toeplitz Operators	p. 495
Operator Equalities for Singular Integral Operators and Their Applications	p. 505
Value Distributions of Complex Functions, Generalizations and Related Topics
On Sets of Range Uniqueness for Entire Functions	p. 515
Analytic Mappings in the Tree Mult (K[x])	p. 519
Using Level Curves to Count Non-Real Zeros of f"	p. 531
The Functional Equation P(f) = Q(g) in a p-Adic Field	p. 539
Conjectures and Counterexamples in Dynamics of Rational Semigroups	p. 549
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