Functions, Spaces, and Expansions

• Mathematical Background.- Normed Vector Spaces.- Banach Spaces.- Hilbert Spaces.- The Lp-spaces.- The Hilbert Space L2.- The Fourier Transform.- An Introduction to Wavelet Analysis.- A Closer Look at Multiresolution Analysis.- B-splines.- Special Functions.- Appendix A.- Appendix B.

From the reviews:“This textbook presents basic mathematical tools of computational harmonic analysis for students of applied mathematics, physics and engineering and presupposes only mild knowledge from linear algebra, calculus and real analysis. … This book is carefully written and surely provides a rewarding read for the intended audience. It also contains a number of well selected exercises at the end of each chapter.” (R. Steinbauer, Monatshefte für Mathematik, Vol. 169 (1), January, 2013)“This textbook aims at representing the mathematical tools of computational harmonic and Fourier analysis in a form that is suitable for students in applied mathematics, physics and engineering. … The book is beautifully written. It contains also a lot of suitable exercises at the end of each section.” (Gerlind Plonka-Hoch, Zentralblatt MATH, Vol. 1231, 2012)“This book is … aimed at students of applied mathematics and engineering. … it is clearly written and it does providea useful summary of the basic properties of the tools it covers. It does a good job of explaining the difference in the various function spaces. It has detailed coverage of wavelets and the related subjects of B-splines and multiresolution analysis, although still without applications.” (Allen Stenger, The Mathematical Association of America, December, 2010)