LEADER 04668nam 22007815 450 001 9910438138603321 005 20200702112822.0 010 $a0-8176-8403-4 024 7 $a10.1007/978-0-8176-8403-7 035 $a(CKB)2670000000315101 035 $a(EBL)1081664 035 $a(OCoLC)823388507 035 $a(SSID)ssj0000870733 035 $a(PQKBManifestationID)11454958 035 $a(PQKBTitleCode)TC0000870733 035 $a(PQKBWorkID)10819325 035 $a(PQKB)10090033 035 $a(DE-He213)978-0-8176-8403-7 035 $a(MiAaPQ)EBC1081664 035 $a(MiAaPQ)EBC6312628 035 $a(PPN)168288761 035 $a(EXLCZ)992670000000315101 100 $a20121211d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on Constructive Approximation $eFourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball /$fby Volker Michel 205 $a1st ed. 2013. 210 1$aBoston, MA :$cBirkhäuser Boston :$cImprint: Birkhäuser,$d2013. 215 $a1 online resource (335 p.) 225 1 $aApplied and Numerical Harmonic Analysis,$x2296-5009 300 $aDescription based upon print version of record. 311 $a0-8176-8402-6 320 $aIncludes bibliographical references and index. 327 $aIntroduction: the Problem to be Solved -- Part I Basics -- Basic Fundamentals?What You Need to Know -- Approximation of Functions on the Real Line -- Part II Approximation on the Sphere -- Basic Aspects -- Fourier Analysis -- Spherical Splines -- Spherical Wavelet Analysis -- Spherical Slepian Functions -- Part III Approximation on the 3D Ball -- Orthonormal Bases -- Splines -- Wavelets for Inverse Problems on the 3D Ball -- The Regularized Functional Matching Pursuit (RFMP) -- References -- Index. 330 $aLectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author?s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth?s or the brain?s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields. 410 0$aApplied and Numerical Harmonic Analysis,$x2296-5009 606 $aApproximation theory 606 $aSpecial functions 606 $aFourier analysis 606 $aPhysics 606 $aNumerical analysis 606 $aApproximations and Expansions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12023 606 $aSpecial Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M1221X 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 615 0$aApproximation theory. 615 0$aSpecial functions. 615 0$aFourier analysis. 615 0$aPhysics. 615 0$aNumerical analysis. 615 14$aApproximations and Expansions. 615 24$aSpecial Functions. 615 24$aFourier Analysis. 615 24$aMathematical Methods in Physics. 615 24$aNumerical Analysis. 676 $a511.4 700 $aMichel$b Volker$4aut$4http://id.loc.gov/vocabulary/relators/aut$0274209 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438138603321 996 $aLectures on Constructive Approximation$92502202 997 $aUNINA