Displaying similar documents to “Exact Asymptotic Behaviour of the Singular Values of Integral Operators With the Kernel Having Singularity on the Diagonal”

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 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 .

Spectrum of the weighted Laplace operator in unbounded domains

Alexey Filinovskiy (2011)

Mathematica Bohemica

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We investigate the spectral properties of the differential operator - r s Δ , s 0 with the Dirichlet boundary condition in unbounded domains whose boundaries satisfy some geometrical condition. Considering this operator as a self-adjoint operator in the space with the norm u L 2 , s ( Ω ) 2 = Ω r - s | u | 2 d x , we study the structure of the spectrum with respect to the parameter s . Further we give an estimate of the rate of condensation of discrete spectra when it changes to continuous.