Displaying similar documents to “A study of an operator arising in the theory of circular plates”

Self-adjoint extensions by additive perturbations

Andrea Posilicano (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let A 𝒩 be the symmetric operator given by the restriction of A to 𝒩 , where A is a self-adjoint operator on the Hilbert space ℋ and 𝒩 is a linear dense set which is closed with respect to the graph norm on D ( A ) , the operator domain of A . We show that any self-adjoint extension A Θ of A 𝒩 such that D ( A Θ ) ∩ D ( A ) = 𝒩 can be additively decomposed by the sum A Θ = A ¯ + T Θ , where both the operators A ¯ and T Θ take values in the strong dual of D ( A ) . The operator A ¯ is the closed extension of A to the whole ℋ whereas T Θ is explicitly...

Spectral properties of a certain class of Carleman operators

S. M. Bahri (2007)

Archivum Mathematicum

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The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space L 2 X , μ and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of A and then using the Stieltjes inversion formula.