Ebook: Complex Harmonic Splines, Periodic Quasi-Wavelets: Theory and Applications

This book, written by our distinguished colleague and friend, Professor Han-Lin Chen of the Institute of Mathematics, Academia Sinica, Beijing, presents, for the first time in book form, his extensive work on complex harmonic splines with applications to wavelet analysis and the numerical solution of boundary integral equations. Professor Chen has worked in Ap­ proximation Theory and Computational Mathematics for over forty years. His scientific contributions are rich in variety and content. Through his publications and his many excellent Ph. D. students he has taken a leader­ ship role in the development of these fields within China. This new book is yet another important addition to Professor Chen's quality research in Computational Mathematics. In the last several decades, the theory of spline functions and their ap­ plications have greatly influenced numerous fields of applied mathematics, most notably, computational mathematics, wavelet analysis and geomet­ ric modeling. Many books and monographs have been published studying real variable spline functions with a focus on their algebraic, analytic and computational properties. In contrast, this book is the first to present the theory of complex harmonic spline functions and their relation to wavelet analysis with applications to the solution of partial differential equations and boundary integral equations of the second kind. The material presented in this book is unique and interesting. It provides a detailed summary of the important research results of the author and his group and as well as others in the field.

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This book presents Complex Harmonic Splines (CHS), which gives an approximation to the Complex Harmonic Function (CHF), in particular the conformal mapping with high accuracy from the unit disc to a domain with arbitrary shape. The volume develops various periodic quasi-wavelets which can be used to solve the Helmholtz integral equation under some boundary conditions with complexity O(N). The last part of the work introduces a class of periodic wavelets with various properties.
Audience: This volume will be of interest to applied mathematicians, physicists and engineers whose work involves approximations and expansions, integral equations, functions of a complex variable and numerical analysis.

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This book presents Complex Harmonic Splines (CHS), which gives an approximation to the Complex Harmonic Function (CHF), in particular the conformal mapping with high accuracy from the unit disc to a domain with arbitrary shape. The volume develops various periodic quasi-wavelets which can be used to solve the Helmholtz integral equation under some boundary conditions with complexity O(N). The last part of the work introduces a class of periodic wavelets with various properties.
Audience: This volume will be of interest to applied mathematicians, physicists and engineers whose work involves approximations and expansions, integral equations, functions of a complex variable and numerical analysis.
Content:
Front Matter....Pages i-xii
Theory and Application of Complex Harmonic Spline Functions....Pages 1-56
Periodic Quasi-Wavelets....Pages 57-118
The Application of Quasi-Wavelets in Solving a Boundary Integral Equation of the Second Kind....Pages 119-163
The Periodic Cardinal Interpolatory Wavelets....Pages 164-211
Back Matter....Pages 212-226

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This book presents Complex Harmonic Splines (CHS), which gives an approximation to the Complex Harmonic Function (CHF), in particular the conformal mapping with high accuracy from the unit disc to a domain with arbitrary shape. The volume develops various periodic quasi-wavelets which can be used to solve the Helmholtz integral equation under some boundary conditions with complexity O(N). The last part of the work introduces a class of periodic wavelets with various properties.
Audience: This volume will be of interest to applied mathematicians, physicists and engineers whose work involves approximations and expansions, integral equations, functions of a complex variable and numerical analysis.
Content:
Front Matter....Pages i-xii
Theory and Application of Complex Harmonic Spline Functions....Pages 1-56
Periodic Quasi-Wavelets....Pages 57-118
The Application of Quasi-Wavelets in Solving a Boundary Integral Equation of the Second Kind....Pages 119-163
The Periodic Cardinal Interpolatory Wavelets....Pages 164-211
Back Matter....Pages 212-226
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