Resumen de Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere

D. Azevedo, Valdir A. Menegatto

• We obtain explicit formulas for the eigenvalues of integral operators generated by continuous dot product kernels defined on the sphere via the usual gamma function. Using them, we present both, a procedure to describe sharp bounds for the eigenvalues and their asymptotic behavior near 0.We illustrate our results with examples, among them the integral operator generated by a Gaussian kernel. Finally, we sketch complex versions of our results to cover the cases when the sphere sits in a Hermitian space.