Displaying similar documents to “Some Estimates of the Remainder in the Expressions for the Eigenvalue Asymptotics of Some Singular Integral Operators”

Exact asymptotic behavior of singular values of a class of integral operators

Milutin R. Dostanić (1999)

Czechoslovak Mathematical Journal

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We find an exact asymptotic formula for the singular values of the integral operator of the form ∫ Ω T ( x , y ) k ( x - y ) · d y L 2 ( Ω ) → L 2 ( Ω ) ( Ω ⊂ ℝ m , a Jordan measurable set) where k ( t ) = k 0 ( ( t 1 2 + t 2 2 + ... t m 2 ) m 2 ) , k 0 ( x ) = x α - 1 L ( 1 x ) , 1 2 - 1 2 m < α < 1 2 and L is slowly varying function with some additional properties. The formula is an explicit expression in terms of L and T .

Eigenvalue distribution for non-self-adjoint operators with small multiplicative random perturbations

Johannes Sjöstrand (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this work we continue the study of the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint (pseudo)differential operators with small random perturbations, by treating the case of multiplicative perturbations in arbitrary dimension. We were led to quite essential improvements of many of the probabilistic aspects.