Feng Dai is currently a professor of mathematics at the University of Alberta, and Yuan Xu is currently a professor of mathematics at the University of Oregon.

• ​​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 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.

From the reviews: "This research monograph is recommended to graduate students, mathematicians, physicists, and engineers who have an interest in analysis and approximation on the sphere, ball, and simplex. ... At the end of each chapter one finds useful 'notes and further results', where the authors present an account of the sources used for the developments in the chapter as well as comments on related results." (P. P. Petrushev, Mathematical Reviews, January, 2014) "The book under review is the most detailed monograph on harmonic analysis, approximation and their applications in the spherical setting. ... This monograph in whole and its various parts can be used both by researchers and by lecturers, for information and ideas by the formers and as a matter for special courses for students by the latters." (Elijah Liflyand, zbMATH, Vol. 1275, 2014)