球面上的調(diào)和分析與逼近

前言

In recent years the research in Fourier Analysis and Approxima-tion Theory has been extended from the classical setting, i.e., from the investigation on Rn and, respectively, to the investigation onmanifolds. Nikol'skii has published a series of papers in this respect.

內(nèi)容概要

The aim of the book "Harmonic Analysis and Approximation on the　Unit Sphere"is:(1)to give a basic introduxtion to the spherical harmonic expansion i.e.the Fourier-Laplace series of functions on the sphere of multidimensional Euclician spaces;(2)to present the main research results obtained in this area by the authors and their co -authors during the period form 1991 to 1999;(3)to provide a basic selfcontained reading material for the graduate students.    This book can serve as a specialty textboku for the graduate students in the realfunction theory group of mathematical departement of universities.

書籍目錄

Chapter1 Preliminaries　1.1 Basicconcepts　1.2 GegenbauerandJacobipolynomials　1.3 JacobipolynomialswithcomplexindicesChapter2 Fourier-LaplaceSeries　2.1 Introduction　2.2 Convergence,Lebesgueconstant　2.3 Cesaromeans(Earlyresults)　2.4 Translationoperatorandmeanoperator　2.5 Maximaltranslationoperator　2.6 ProjectionoperatorsChapter3 EquiconvergentOperatorsofCesaaroMeans　3.1 Definition　3.2 Localization　3.3 Pointwiseconvergence　3.4 MaximaloperatorEaanda.e.convergence　3.5 ApplicationtolinearsummabilityChapter4 ConstructivePropericalfunctions　4.1 Bestapproximationoperator　4.2 PointwiseDerivatives　4.3 Fractionalderivativeandintegral　4.4 Fractionalintegralsofvariableorder　4.5 Modulusofcontinuity　4.6 DerivativesandfinitedifferencesChapter5 JacksonTypeTheorems　5.1 JacksoninequalityandK-functional　5.2 DifferenceandspaceH`Chapter6 ApproximationbyLinearMeans　6.1 Almosteverywhereapproximation　6.2 Approximationinnorm　6.3 ThedelaValleePoussinMeansReferencesIndex

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