000 03447nam a22005055i 4500
001 978-1-4614-6660-4
003 DE-He213
005 20140220082825.0
007 cr nn 008mamaa
008 130417s2013 xxu| s |||| 0|eng d
020 _a9781461466604
_9978-1-4614-6660-4
024 7 _a10.1007/978-1-4614-6660-4
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aDai, Feng.
_eauthor.
245 1 0 _aApproximation Theory and Harmonic Analysis on Spheres and Balls
_h[electronic resource] /
_cby Feng Dai, Yuan Xu.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXVIII, 440 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Monographs in Mathematics,
_x1439-7382
505 0 _a1 Spherical Harmonics -- 2 Convolution and Spherical Harmonic Expansion -- 3 Littlewood-Paley Theory and Multiplier Theorem -- 4 Approximation on the Sphere -- 5 Weighted Polynomial Inequalities -- 6 Cubature Formulas on Spheres -- 7 Harmonic Analysis Associated to Reflection Groups -- 8 Boundedness of Projection Operator and Cesàro Means -- 9 Projection Operators and Cesàro Means in L^p Spaces -- 10 Weighted Best Approximation by Polynomials -- 11 Harmonic Analysis on the Unit Ball -- 12 Polynomial Approximation on the Unit Ball -- 13 Harmonic Analysis on the Simplex -- 14 Applications -- A Distance, Difference and Integral Formulas -- B Jacobi and Related Orthogonal Polynomials -- References -- Index -- Symbol Index.
520 _aThis monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area.  While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes.  The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aFourier analysis.
650 0 _aFunctions, special.
650 1 4 _aMathematics.
650 2 4 _aAnalysis.
650 2 4 _aApproximations and Expansions.
650 2 4 _aFourier Analysis.
650 2 4 _aSpecial Functions.
700 1 _aXu, Yuan.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461466598
830 0 _aSpringer Monographs in Mathematics,
_x1439-7382
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-6660-4
912 _aZDB-2-SMA
999 _c95721
_d95721