Displaying similar documents to “The Hahn-Exton q-Bessel function as the characteristic function of a Jacobi matrix”

Extensions, dilations and functional models of infinite Jacobi matrix

B. P. Allahverdiev (2005)

Czechoslovak Mathematical Journal

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A space of boundary values is constructed for the minimal symmetric operator generated by an infinite Jacobi matrix in the limit-circle case. A description of all maximal dissipative, accretive and selfadjoint extensions of such a symmetric operator is given in terms of boundary conditions at infinity. We construct a selfadjoint dilation of maximal dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of...

A study of an operator arising in the theory of circular plates

Leopold Herrmann (1988)

Aplikace matematiky

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The operator L 0 : D L 0 ⊂ H → H , L 0 u = 1 r d d r r d d r 1 r d d r r d u d r , D L 0 = { u ∈ C 4 ( [ 0 , R ] ) , u ' ( 0 ) = u ' ' ' ' ( 0 ) = 0 , u ( R ) = u ' ( R ) = 0 } , H = L 2 , r ( 0 , R ) is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on L 0 (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types L 0 u = g and u t t + L 0 u = g , respectively.