Approximation Theory and Harmonic Analysis on Spheres and Related Domains
نویسنده
چکیده
There have been continuing researches in approximation theory and harmonic analysis on the unit sphere throughout the last century. For approximation theory, one of the historical highlights is the complete characterization of best approximation by polynomials on the sphere in terms of a modulus of smoothness defined via the spherical means, the accumulation point of decades of works by many authors and finally materialized in [13, 1994]. For harmonic analysis on the sphere, besides the general results that hold for the homogeneous spaces, including the sphere, the essential results are those on multiplier theorems and convergence of projection operators and the Cesàro means in [1, 1972] and [14, 1986]. In recent years analysis on the sphere has been revitalized by applications in applied mathematics, such as earth sciences, computational mathematics and statistics. The topics have fruitful connections with many branches of mathematics, such as numerical integration, computer tomography, coding theory, data fitting, special functions, group representation, spectral theory, random matrices, and differential equations.
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تاریخ انتشار 2011