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Operator theory --- Functional analysis --- 512.55 --- 517.98 --- Banach lattices --- Banach modules (Algebra) --- Banach algebras --- Modules (Algebra) --- Lattices, Banach --- Lattice theory --- Rings and modules --- Functional analysis and operator theory --- 517.98 Functional analysis and operator theory --- 512.55 Rings and modules --- Banach, Modules de --- Operator theory. --- Opérateurs, Théorie des --- Banach lattices. --- Banach, Treillis de --- Banach, Modules de. --- Opérateurs, Théorie des. --- Banach, Treillis de.

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Analytical spaces --- Ordered algebraic structures --- Banach spaces --- Banach modules (Algebra) --- Categories (Mathematics) --- 517.986 --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Functions of complex variables --- Generalized spaces --- Banach algebras --- Modules (Algebra) --- Topological algebras. Theory of infinite-dimensional representations --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Analyse fonctionnelle --- Functional analysis --- Functional analysis. --- Catégories (mathématiques)

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Motivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools; they may be orthogonal or have redundancies (e.g., frames from signal analysis). Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topics are selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure and applied mathematics while also of interest to engineers. The book is organized into five sections that move from the theoretical underpinnings of the subject, through geometric connections to tilings, lattices and fractals, and concludes with analyses of computational schemes used in communications engineering. Within each section, individual chapters present new research, provide relevant background material, and point to new trends and open questions. Contributors: C. Benson, M. Bownik, V. Furst, V.W. Guillemin, B. Han, C. Heil, J.A. Hogan, P.E.T. Jorgensen, K. Kornelson, J.D. Lakey, D.R. Larson, K.D. Merrill, J.A. Packer, G. Ratcliff, K. Shuman, M.-S. Song, D.W. Stroock, K.F. Taylor, E. Weber, X. Zhang.

Wavelets (Mathematics) --- Frames (Combinatorial analysis) --- Representations of Banach modules. --- Banach modules (Algebra) --- Combinatorial designs and configurations --- Wavelet analysis --- Harmonic analysis --- Fourier analysis. --- Harmonic analysis. --- Mathematics. --- Functional analysis. --- Mathematical Modeling and Industrial Mathematics. --- Fourier Analysis. --- Signal, Image and Speech Processing. --- Abstract Harmonic Analysis. --- Applications of Mathematics. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Analysis, Fourier --- Mathematical models. --- Signal processing. --- Image processing. --- Speech processing systems. --- Applied mathematics. --- Engineering mathematics. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Engineering --- Engineering analysis --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Models, Mathematical --- Simulation methods