On optimal bound of Foschi’s quadratic functional in higher-dimensional spheres

Annali di Matematica Pura ed Applicata (1923 -)（2021）

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摘要

In proving his theorem on global maximizers for the sphere adjoint Fourier restriction inequality, D. Foschi studied some quadratic functional and determined its optimal bound. In this note we extend to higher-dimensional spheres his results on this quadratic functional.

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关键词

Spectral decomposition, Spherical harmonics, Gegenbauer polynomial, Generalized hypergeometric functions, Saalschüz theorem, Sphere adjoint Fourier restriction inequality, Primary 33C45, 33C55

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