Summary
In this paper the trace equations
arising in the Hilbert-Schmidt theory of Fredholm integral equations are extended to certain classes of compact operators K(λ) on Hilbert space ℋ which are meromorphic functions of the eigenvalue parameter λ. The operator K(λ) is the sum of an operator valued polynomial H(λ) plus an operator P(λ) which is a meromorphic function of λ and has finite dimensional range for each fixed λ. The theory is constructed so that if ℋ=L2[0, 1] and if
where the Hi are integral operators derivable from corresponding Lebesgue square integrable kernels hi(x, y), then one can systematically take advantage of various regularity conditions that some of the kernels hi(x, y) may have in improving the results.
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Entrata in Redazione il 20 novembre 1974.
The research reported in this paper was partially supported by the National Science Foundation under Grant Number GP-33679X.
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Laginestra, A.V., Boyce, W.E. Convergence and evaluation of sums of reciprocal powers of eigenvalues of certain compact operators (on Hilbert space) which are meromorphic functions of the eigenvalue parameter. Annali di Matematica 111, 229–305 (1976). https://doi.org/10.1007/BF02411821
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DOI: https://doi.org/10.1007/BF02411821