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On Kato non-singularity

Robin Harte (1996)

Studia Mathematica

An exactness lemma offers a simplified account of the spectral properties of the "holomorphic" analogue of normal solvability.

On L w 2 -quasi-derivatives for solutions of perturbed general quasi-differential equations

Sobhy El-sayed Ibrahim (1999)

Czechoslovak Mathematical Journal

This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equation of n th order with complex coefficients M [ y ] - λ w y = w f ( t , y [ 0 ] , ... , y [ n - 1 ] ) , t [ a , b ) provided that all r th quasi-derivatives of solutions of M [ y ] - λ w y = 0 and all solutions of its normal adjoint M + [ z ] - λ ¯ w z = 0 are in L w 2 ( a , b ) and under suitable conditions on the function f .

On limits of L p -norms of an integral operator

Pavel Stavinoha (1994)

Applications of Mathematics

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.

On Minimizing ||S−(AX−XB)||Pp

Mecheri, Salah (2000)

Serdica Mathematical Journal

In this paper, we minimize the map Fp (X)= ||S−(AX−XB)||Pp , where the pair (A, B) has the property (F P )Cp , S ∈ Cp , X varies such that AX − XB ∈ Cp and Cp denotes the von Neumann-Schatten class.

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