A REVIEW ON DECAY RATES OF EIGENVALUES OF INTEGRAL OPERATORS ON DIFFERENT SPACES

Let K(x; y) : X £ X ! C be a positive definite kernel of an integral operator K, where X can be an unbounded interval on R or metric space endowed with a measure. If the Kernel K 2 A, then the corresponding integral operator is trace-class and compact. The result covers the case when X is a subset of the sphere Sm endowed with the induced lebesgue measure. Lastly, we consider and compare decay rates of integral operators in different conditions.