000 05496nam a22006135i 4500
001 978-3-319-55556-0
003 DE-He213
005 20181204134423.0
007 cr nn 008mamaa
008 170810s2017 gw | s |||| 0|eng d
020 _a9783319555560
_9978-3-319-55556-0
024 7 _a10.1007/978-3-319-55556-0
_2doi
040 _aISI Library, Kolkata
050 4 _aQA403-403.3
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKD
_2thema
082 0 4 _a515.785
_223
245 1 0 _aRecent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science
_h[electronic resource] :
_bNovel Methods in Harmonic Analysis, Volume 2 /
_cedited by Isaac Pesenson, Quoc Thong Le Gia, Azita Mayeli, Hrushikesh Mhaskar, Ding-Xuan Zhou.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2017.
300 _aXIV, 510 p. 81 illus., 25 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied and Numerical Harmonic Analysis,
_x2296-5009
505 0 _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.
520 _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.
650 0 _aHarmonic analysis.
650 0 _aFourier analysis.
650 0 _aNumerical analysis.
650 0 _aBig data.
650 0 _aComputer science.
650 1 4 _aAbstract Harmonic Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12015
650 2 4 _aFourier Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12058
650 2 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
650 2 4 _aBig Data.
_0http://scigraph.springernature.com/things/product-market-codes/I29120
650 2 4 _aComputational Science and Engineering.
_0http://scigraph.springernature.com/things/product-market-codes/M14026
700 1 _aPesenson, Isaac.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aLe Gia, Quoc Thong.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aMayeli, Azita.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aMhaskar, Hrushikesh.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aZhou, Ding-Xuan.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319555553
776 0 8 _iPrinted edition:
_z9783319555577
776 0 8 _iPrinted edition:
_z9783319856933
830 0 _aApplied and Numerical Harmonic Analysis,
_x2296-5009
856 4 0 _uhttps://doi.org/10.1007/978-3-319-55556-0
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c427359
_d427359