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On limits of \(L_ p\)-norms of an integral operator. (English) Zbl 0816.47055

Summary: A recurrence relation for the computation of the \(L_ p\)-norms of an Hermitian Fredholm integral operator is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the \(L_ p\)-norms for the approximation of the spectral radius of this operator an a priori and an a posteriori bound for the error are obtained. Some properties of the a posteriori bound are discussed.

MSC:

47G10 Integral operators
47A53 (Semi-) Fredholm operators; index theories
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
47A10 Spectrum, resolvent

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REDUCE
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References:

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