Applied and Numerical Harmonic Analysis

Lectures on Constructive Approximation

Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball

Authors: Michel, Volker

  • Combines an explanation of classical and modern approximation methods for Euclidean and spherical geometries
  • Detailed explanations and illustrations included to optimize the understanding of topics
  • Concentrates on the essentials for a course
  • Uses examples of data sets to explain the tasks, challenges, advantages, and disadvantages of the methods presented
  • First work that explicitly treats approximation methods on the ball
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eBook $59.99
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  • ISBN 978-0-8176-8403-7
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  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-0-8176-8402-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
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About this Textbook

Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets.

Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include:

* the advantages and disadvantages of Fourier, spline, and wavelet methods

* theory and numerics of orthogonal polynomials on intervals, spheres, and balls

* cubic splines and splines based on reproducing kernels

* multiresolution analysis using wavelets and scaling functions

This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.

About the authors

Dr. Volker Michel teaches at University of Siegen

Reviews

From the book reviews:

“This is a constructive approach to approximation by Fourier series (orthogonal polynomials), splines and wavelets. … The basis functions are illustrated with many color plots and the proofs are fully written out. … This is a clear introduction to subjects that are not easily found in other textbooks at this level. Obviously it is of interest for geophysical applications.” (Adhemar Bultheel, zbMATH, Vol. 1295, 2014)

“The textbook Lectures on constructive approximation teaches the basics and details of Fourier, spline, and wavelet methods on the real line, the sphere, and the ball. … The style of the book is clearly that of a textbook, since the author makes a great effort to make very complicated concepts comprehensible to the reader. Throughout the book, numerous numerical examples and graphical illustrations support the explanations. This book is appropriate for applied mathematicians and numerical analysts as well as for geoscientists and engineers.” (Willi Freeden, Mathematical Reviews, August, 2013)

Table of contents (12 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-0-8176-8403-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-0-8176-8402-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on Constructive Approximation
Book Subtitle
Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball
Authors
Series Title
Applied and Numerical Harmonic Analysis
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-8403-7
DOI
10.1007/978-0-8176-8403-7
Hardcover ISBN
978-0-8176-8402-0
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XVI, 326
Number of Illustrations and Tables
2 b/w illustrations, 5 illustrations in colour
Topics