Displaying similar documents to “On a class of generalized Laguerre's polynomials”

Logarithmic density of a sequence of integers and density of its ratio set

Ladislav Mišík, János T. Tóth (2003)

Journal de théorie des nombres de Bordeaux

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In the paper sufficient conditions for the ( R ) -density of a set of positive integers in terms of logarithmic densities are given. They differ substantially from those derived previously in terms of asymptotic densities.

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.