Search results for " rigged Hilbert spaces"

showing 2 items of 2 documents

Bessel sequences, Riesz-like bases and operators in Triplets of Hilbert spaces

2016

Riesz-like bases for a triplet of Hilbert spaces are investigated, in connection with an analogous study for more general rigged Hilbert spaces performed in a previous paper. It is shown, in particular, that every \(\omega \)-independent, complete (total) Bessel sequence is a (strict) Riesz-like basis in a convenient triplet of Hilbert spaces. An application to non self-adjoint Schrodinger-type operators is considered. Moreover, some of the simplest operators we can define by them and their dual bases are studied.

Pure mathematicsSequenceBasis (linear algebra)010308 nuclear & particles physics010102 general mathematicsHilbert spaceRiesz bases quasi-Hermitian operators rigged Hilbert spaces01 natural sciencesSchauder basissymbols.namesakeSettore MAT/05 - Analisi Matematica0103 physical sciencessymbols0101 mathematicsConnection (algebraic framework)Bessel functionMathematics
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On non-self-adjoint operators defined by Riesz bases in Hilbert and rigged Hilbert spaces

2018

In this paper we discuss some results on non self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that their eigenvectors form Riesz bases of a certain Hilbert space. Also, we exhibit a generalization of those results to the case of rigged Hilbert spaces, and we also consider the problem of the factorization of the aforementioned Hamiltonians in terms of generalized lowering and raising operators.

Pure mathematicssymbols.namesakeNon self-adjoint Hamiltonians Riesz bases rigged Hilbert spacesSettore MAT/05 - Analisi MatematicaHilbert spacesymbolsSelf-adjoint operatorMathematics
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