Sharp inequalities of singular values of smooth kernels
The authors consider the inequalities of singular values \(s_n(K)\) of the integral operators \(K\) with smooth \(L^2\) kernels. The singular values \(s_n(K)\) are the positive eigenvalues of the positive square root of \(K^*\)K. The inequalities are obtained and shown by examples to be sharp if the kernels satisfy also certain boundary conditions. The results of the paper are based on an idea of Gohberg-Krein by which the singular values of the integral operators are interrelated to the eigenvalues of some two point boundary value problems.
scientific article; zbMATH DE number 1346929