Uniform pointwise estimates for ultraspherical polynomials
Copyright policy )Uniform pointwise estimates for ultraspherical polynomials
We prove pointwise bounds for two-parameter families of Jacobi polynomials. Our bounds imply estimates for a class of functions arising from the spectral analysis of distinguished Laplacians and sub-Laplacians on the unit sphere in arbitrary dimension, and are instrumental in the proof, discussed in a companion paper, of sharp multiplier theorems for those operators.
- University of Birmingham United Kingdom
- University of Padua Italy
- Polytechnic University of Turin Italy
Spectral problems; spectral geometry; scattering theory on manifolds, spherical harmonics, 33C45, 33C55 (Primary) 42C05, 58J50 (Secondary), Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Mathematics - Classical Analysis and ODEs, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, spectral problems, Spherical harmonics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Mathematics
Spectral problems; spectral geometry; scattering theory on manifolds, spherical harmonics, 33C45, 33C55 (Primary) 42C05, 58J50 (Secondary), Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Mathematics - Classical Analysis and ODEs, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, spectral problems, Spherical harmonics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Mathematics
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