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 textbok

Chapter1 Preliminaries
1.1 Basicconcepts
1.2 GegenbauerandJacobipolynomials
1.3 Jacobipolynomialswithcomplexindices
Chapter2 Fourier-LaplaceSeries
2.1 Introduction
2.2 Convergence,Lebesgueconstant
2.3 Cesaromeans(Earlyresults)
2.4 Translationoperatorandmeanoperator
2.5 Maximaltranslationoperator
2.6 Projectionoperators
Chapter3 EquiconvergentOperatorsofCesaaroMeans
3.1 Definition
3.2 Localization
3.3 Pointwiseconvergence
3.4 MaximaloperatorEaanda.e.convergence
3.5 Applicationtolinearsummability
Chapter4 ConstructivePropericalfunctions
4.1 Bestapproximationoperator
4.2 PointwiseDerivatives
4.3 Fractionalderivativeandintegral
4.4 Fractionalintegralsofvariableorder
4.5 Modulusofcontinuity
4.6 Derivativesandfinitedifferences
Chapter5 JacksonTypeTheorems
5.1 JacksoninequalityandK-functional
5.2 DifferenceandspaceH`
Chapter6 ApproximationbyLinearMeans
6.1 Almosteverywhereapproximation
6.2 Approximationinnorm
6.3 ThedelaValleePoussinMeans
References
Index