Abstract
Let k(x, y) be the positive definite kernel of an integral operator on an unbounded interval of ℝ. If k belongs to class 
defined below, the corresponding operator is compact and trace class. We establish two results relating smoothness of k and its decay rate at infinity along the diagonal with the decay rate of the eigenvalues. The first result deals with the Lipschitz case; the second deals with the uniformly C1 case. The optimal results known for compact intervals are recovered as special cases, and the relevance of these results for Fourier transforms is pointed out.
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Buescu, J., Paixão, A. Eigenvalues of Positive Definite Integral Operators on Unbounded Intervals. Positivity 10, 627–646 (2006). https://doi.org/10.1007/s11117-005-0040-z
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DOI: https://doi.org/10.1007/s11117-005-0040-z