Angličtina
The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book elucidates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows one to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical prerequisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts.§Features:§Rigorous proofs with consistent assumptions about the mathematical background of the reader (does not assume familiarity with Hilbert spaces or Lebesgue measure).§Complete background material on is offered on Fourier analysis topics.§ Wavelets are presented first on the continuous domain and later restricted to the discrete domain for improved motivation and understanding of discrete wavelet transforms and applications.§Special appendix, "Excursions in Wavelet Theory," provides a guide to current literature on the topic.§Over 170 exercises guide the reader through the text.§An Introduction to Wavelet Analysis is an ideal text/reference for a broad audience of advanced students and researchers in applied mathematics, electrical engineering, computational science, and physical sciences. It is also suitable as a self-study reference guide for professionals.
