LEADER 04761nam 2200697 a 450 001 9910782094203321 005 20200520144314.0 010 $a1-281-86132-4 010 $a9786611861322 010 $a0-8176-4683-3 024 7 $a10.1007/978-0-8176-4683-7 035 $a(CKB)1000000000492099 035 $a(EBL)364264 035 $a(OCoLC)288469101 035 $a(SSID)ssj0000236189 035 $a(PQKBManifestationID)11215573 035 $a(PQKBTitleCode)TC0000236189 035 $a(PQKBWorkID)10173315 035 $a(PQKB)11270241 035 $a(DE-He213)978-0-8176-4683-7 035 $a(MiAaPQ)EBC364264 035 $a(Au-PeEL)EBL364264 035 $a(CaPaEBR)ebr10253369 035 $a(CaONFJC)MIL186132 035 $a(PPN)128122854 035 $a(EXLCZ)991000000000492099 100 $a20090216d2008 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 00$aRepresentations, wavelets, and frames$b[electronic resource] $ea celebration of the mathematical work of Lawrence W. Baggett /$fPalle E.T. Jorgensen, Kathy D. Merrill, Judith A. Packer, editors 205 $a1st ed. 2008. 210 $aBoston $cBirkha?user$d2008 215 $a1 online resource (351 p.) 225 1 $aApplied and numerical harmonic analysis 300 $aDescription based upon print version of record. 311 $a0-8176-4682-5 320 $aIncludes bibliographical references and index. 327 $aClassical and Abstract Harmonic Analysis -- Some Riemann Sums Are Better Than Others -- Gelfand Pairs Associated with Finite Heisenberg Groups -- Groups with Atomic Regular Representation -- Wavelet Transforms and Admissible Group Representations -- Frames and Multiresolution Structures -- The Density Theorem and the Homogeneous Approximation Property for Gabor Frames -- Recent Developments on Dual Wavelet Frames -- Characteristic Wavelet Equations and Generalizations of the Spectral Function -- Baggett?s Problem for Frame Wavelets -- Wavelet Sets -- Simple Wavelet Sets for Scalar Dilations in ?2 -- Interpolation Maps and Congruence Domains for Wavelet Sets -- Applications to Dynamical Systems and C*-Algebras -- Orthogonal Exponentials for Bernoulli Iterated Function Systems -- A Survey of Projective Multiresolution Analyses and a Projective Multiresolution Analysis Corresponding to the Quincunx Lattice -- Signal and Image Processing -- Sampling and Time-Frequency Localization of Band-Limited and Multiband Signals -- Entropy Encoding in Wavelet Image Compression. 330 $aMotivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools; they may be orthogonal or have redundancies (e.g., frames from signal analysis). Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topics are selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure and applied mathematics while also of interest to engineers. The book is organized into five sections that move from the theoretical underpinnings of the subject, through geometric connections to tilings, lattices and fractals, and concludes with analyses of computational schemes used in communications engineering. Within each section, individual chapters present new research, provide relevant background material, and point to new trends and open questions. Contributors: C. Benson, M. Bownik, V. Furst, V.W. Guillemin, B. Han, C. Heil, J.A. Hogan, P.E.T. Jorgensen, K. Kornelson, J.D. Lakey, D.R. Larson, K.D. Merrill, J.A. Packer, G. Ratcliff, K. Shuman, M.-S. Song, D.W. Stroock, K.F. Taylor, E. Weber, X. Zhang. 410 0$aApplied and numerical harmonic analysis. 606 $aWavelets (Mathematics) 606 $aFrames (Combinatorial analysis) 606 $aRepresentations of Banach modules 615 0$aWavelets (Mathematics) 615 0$aFrames (Combinatorial analysis) 615 0$aRepresentations of Banach modules. 676 $a515.2433 701 $aJørgensen$b Palle E. T.$f1947-$01469263 701 $aMerrill$b Kathy Donovan$0768256 701 $aPacker$b Judith A$01469264 701 $aBaggett$b Lawrence W.$f1939-$066708 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910782094203321 996 $aRepresentations, wavelets, and frames$93680690 997 $aUNINA