Wavelet Theory

Igor Iakovlevič Novikov (mathématicien).) · Vladimir I︠U︡rʹevich Protasov · Marii︠a︡ Aleksandrovna Skopina

2011년 1월 · Translations of Mathematical Monographs 239권 · American Mathematical Soc.

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Wavelet theory lies on the crossroad of pure and computational mathematics, with connections to audio and video signal processing, data compression, and information transmission. The present book is devoted to a systematic exposition of modern wavelet theory. It details the construction of orthogonal and biorthogonal systems of wavelets and studies their structural and approximation properties, starting with basic theory and ending with special topics and problems. The book also presents some applications of wavelets. Historical commentary is supplied for each chapter in the book, and most chapters contain exercises. The book is intended for professional mathematicians and graduate students working in functional analysis and approximation theory. It is also useful for engineers applying wavelet theory in their work. Prerequisites for reading the book consist of graduate courses in real and functional analysis.