LEADER 05744nam 22007335 450 001 9910254305403321 005 20220413221717.0 010 $a3-319-55556-1 024 7 $a10.1007/978-3-319-55556-0 035 $a(CKB)3710000001631049 035 $a(MiAaPQ)EBC4944149 035 $a(DE-He213)978-3-319-55556-0 035 $z(PPN)258853034 035 $a(PPN)203850882 035 $a(EXLCZ)993710000001631049 100 $a20170810d2017 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aRecent applications of harmonic analysis to function spaces, differential equations, and data science $enovel methods in harmonic analysis, volume 2 /$fedited by Isaac Pesenson, Quoc Thong Le Gia, Azita Mayeli, Hrushikesh Mhaskar, Ding-Xuan Zhou 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2017. 215 $a1 online resource (512 pages) $cillustrations 225 1 $aApplied and Numerical Harmonic Analysis,$x2296-5009 311 $a3-319-55555-3 320 $aIncludes bibliographical references at the end of each chapters. 327 $aIntroduction -- Characterization of Gevrey Regularity by a Class of FBI Transforms -- A Novel Mathematical Approach to the Theory of Translation Invariant Linear Systems -- Asymptotic Behaviour of the Fourier Transform of a Function of Bounded Variation -- Convergence and Regularization of Sampling Series -- Harmonic Analysis in Non-Euclidean Spaces: Theory and Application -- An Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes -- Sheaf and Duality Methods for Analyzing Multi-Model Systems -- On Boundary-Value Problems for a Partial Differential Equation with Caputo and Bessel Operator -- On the Solvability of the Zaremba Problem in Infinite Sectors and the Invertibility of Associated Singular Integral Operators -- On the Solution of the Oblique Derivative Problem by Constructive Runge-Walsh Concepts -- An Overview of Numerical Acceleration Techniques for Non-Linear Dimension Reduction -- Adaptive Density Estimation on the Circle by Nearly-Tight Frames -- Interactions between Kernels, Frames, and Persistent Homology -- Multi-Penalty Regularization for Detecting Relevant Variables -- Stable Likelihood Computation for Gaussian Random Fields. 330 $aThe second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge?Walsh theorem for the oblique derivative problem of physical geodesy. 410 0$aApplied and Numerical Harmonic Analysis,$x2296-5009 606 $aHarmonic analysis 606 $aFourier analysis 606 $aNumerical analysis 606 $aBig data 606 $aComputer mathematics 606 $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aBig Data$3https://scigraph.springernature.com/ontologies/product-market-codes/I29120 606 $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026 615 0$aHarmonic analysis. 615 0$aFourier analysis. 615 0$aNumerical analysis. 615 0$aBig data. 615 0$aComputer mathematics. 615 14$aAbstract Harmonic Analysis. 615 24$aFourier Analysis. 615 24$aNumerical Analysis. 615 24$aBig Data. 615 24$aComputational Science and Engineering. 676 $a515.2433 702 $aPesenson$b Isaac$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aLe Gia$b Quoc Thong$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aMayeli$b Azita$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aMhaskar$b Hrushikesh$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aZhou$b Ding-Xuan$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254305403321 996 $aRecent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science$92162753 997 $aUNINA