Multivariate Wavelet Frames

VLADIMIR PROTASOV is a professor at the Department of Mechanics and Mathematics, Moscow State University, where he also received his Ph.D. in 1999. He was awarded his D.Sc. at St. Petersburg Department of V.A. Steklov Institute of Mathematics, the Russian Academy of Sciences (2006). His research areas include functional analysis, Fourier analysis, wavelets, matrix theory, optimization, convex geometry, and combinatorics. He is the author of more than 70 research papers, 2 monographs, and more than 20 popular and educational publications, including 4 books. He is a member of the editorial board of Sbornik: Mathematics and Quantum Journal.MARIA SKOPINA is a professor at the Department of Applied Mathematics and Control Processes, St. Petersburg State University. She received her Ph.D. there in 1980 and her D.Sc. from St. Petersburg Department of V.A. Steklov Institute of Mathematics, the Russian Academy of Sciences in 2000. Her main research interests are wavelets, Fourier series, approximation theory and abstract harmonic analysis. She is the author of more than 70 research papers and the monograph “Wavelet Theory,” which was published in Russian in 2005 and translated into English by the American Mathematical Society (AMS) in 2011. She is a member of the St. Petersburg Mathematical Society and the AMS. She is also an associate editor for the International Journal of Wavelets, Multiresolution and Information Processing (IJWMIP) and has organized four international conferences on “Wavelets and Applications.”ALEKSANDR KRIVOSHEIN received his Ph.D. from St. Petersburg State University in 2013 and is currently an associate professor at the Department of Applied Mathematics and Control Processes there. His main research interests include wavelets and their applications to signal processing. He is the author of 10 research papers.

“This book provides the mathematical theory for multivariate wavelets and framelets, presents several algorithms to construct them, and illustrates the theory and algorithms by many detailed examples. It will be useful for researchers who study multivariate wavelets and framelets.” (Bin Han, Mathematical Reviews, October, 2017)

• Chapter 1. Bases and Frames in Hilbert Spaces.- Chapter 2. MRA-based Wavelet Bases and Frames.- Chapter 3. Construction of Wavelet Frames.- Chapter 4. Frame-like Wavelet Expansions.- Chapter 5. Symmetric Wavelets.- Chapter 6. Smoothness of Wavelets.- Chapter 7. Special Questions.