Lectures on Constructive Approximation Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball /

• Main Author: Michel, Volker. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Boston : Birkhũser Boston : Imprint: Birkhũser, 2013.
• Series: Applied and Numerical Harmonic Analysis
• Subjects: Mathematics.; Fourier analysis.; Functions, special.; Numerical analysis.; Mathematical physics.; Approximations and Expansions.; Special Functions.; Fourier Analysis.; Mathematical Methods in Physics.; Numerical Analysis.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-8176-8403-7

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<U+0019>s lectures on classical approximation methods based on orth...

Table of Contents:

• Introduction: the Problem to be Solved
• Part I Basics
• Basic Fundamentals<U+0014>What You Need to Know
• Approximation of Functions on the Real Line
• Part II Approximation on the Sphere
• Basic Aspects
• Fourier Analysis
• Spherical Splines
• Spherical Wavelet Analysis
• Spherical Slepian Functions
• Part III Approximation on the 3D Ball
• Orthonormal Bases
• Splines
• Wavelets for Inverse Problems on the 3D Ball
• The Regularized Functional Matching Pursuit (RFMP)
• References
• Index.