{"id":33169,"date":"2020-08-21T12:55:22","date_gmt":"2020-08-21T12:55:22","guid":{"rendered":"http:\/\/tugraztestweb.asol.at\/gesamtverzeichnis\/unkategorisiert\/schroedinger-operators-and-singular-infinite-rank-perturbations-2\/"},"modified":"2020-08-21T14:56:22","modified_gmt":"2020-08-21T12:56:22","slug":"schroedinger-operators-and-singular-infinite-rank-perturbations-ebook","status":"publish","type":"product","link":"https:\/\/tugraztestweb.asol.at\/en\/gesamtverzeichnis\/technische-mathematik-und-technische-physik\/schroedinger-operators-and-singular-infinite-rank-perturbations-ebook\/","title":{"rendered":"Schr\u00f6dinger operators and singular infinite rank perturbations"},"content":{"rendered":"

Sorry, this entry is only available in Deutsch<\/a>.<\/p>

The present thesis consist of two parts. The abstract part is concerned
\nwith singular infinite rank perturbations of selfadjoint operators.
\nStarting with a selfadjoint operator we construct a chain of rigged
\nHilbert spaces and investigate some of their properties. Afterwards this
\n operator is perturbed by another operator whose range is contained in
\none of the rigged Hilbert spaces with negative index. The rigorous
\ndefinition of such a perturbation is done with the help of ordinary and
\ngeneralized boundary triples. Hereby we have to distinguish different
\ncases, depending on the index mentioned above.
Using this abstract
\napproach we consider in the second part of this thesis Schr\u00f6dinger
\noperators with delta-interactions supported on manifolds, give criteria
\nfor selfadjointness and investigate their spectra. Also here we have to
\ndistinguish different cases, depending on the codimension of the
\nmanifold. Special attention is paid to the case that the manifold has
\ncodimension two, in particular to the case of a closed curve in the
\nthree-dimensional Euclidean space.<\/p>","protected":false},"excerpt":{"rendered":"

Sorry, this entry is only available in Deutsch<\/a>.<\/p>\n

The present thesis consist of two parts. The abstract part is concerned
\nwith singular infinite rank perturbations of selfadjoint operators.
\nStarting with a selfadjoint operator we construct a chain of rigged
\nHilbert spaces and investigate some of their properties. Afterwards this
\n operator is perturbed by another operator whose range is contained in
\none of the rigged Hilbert spaces with negative index. The rigorous
\ndefinition of such a perturbation is done with the help of ordinary and
\ngeneralized boundary triples. Hereby we have to distinguish different
\ncases, depending on the index mentioned above.
Using this abstract
\napproach we consider in the second part of this thesis Schr\u00f6dinger
\noperators with delta-interactions supported on manifolds, give criteria
\nfor selfadjointness and investigate their spectra. Also here we have to
\ndistinguish different cases, depending on the codimension of the
\nmanifold. Special attention is paid to the case that the manifold has
\ncodimension two, in particular to the case of a closed curve in the
\nthree-dimensional Euclidean space.<\/p>\n","protected":false},"featured_media":40129,"comment_status":"open","ping_status":"closed","template":"","meta":[],"yoast_head":"\n\n\n\n\n\n\n\n\n\n\t\n\t\n\n\n\t\n