Approximation Theory and Harmonic Analysis on Spheres and Balls

1 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 Cesaro Means.- 9 Projection Operators and Cesaro 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