Browsing by Subject "Dirac operator"

Now showing 1 - 3 of 3

Open Access
Closely embedded Krein spaces and applications to Dirac operators
(Elsevier, 2011-04-15) Cojuhari, P.; Gheondea, A.
Motivated by energy space representation of Dirac operators, in the sense of K. Friedrichs, we recently introduced the notion of closely embedded Krein spaces. These spaces are associated to unbounded selfadjoint operators that play the role of kernel operators, in the sense of L Schwartz, and they are special representations of induced Krein spaces. In this article we present a canonical representation of closely embedded Krein spaces in terms of a generalization of the notion of operator range and obtain a characterization of uniqueness. When applied to Dirac operators, the results differ according to a mass or a massless particle in a dramatic way: in the case of a particle with a nontrivial mass we obtain a dual of a Sobolev type space and we have uniqueness, while in the case of a massless particle we obtain a dual of a homogenous Sobolev type space and we lose uniqueness. (C) 2010 Elsevier Inc. All rights reserved.
Open Access
Embeddings, operator ranges, and Dirac operators
(Springer Basel, 2011) Cojuhari, P.; Gheondea, A.
Motivated by energy space representation of Dirac operators, in the sense of K. Friedrichs, we recently introduced the notion of closely embedded Kreǐn spaces. These spaces are associated to unbounded selfadjoint operators that play the role of kernel operators, in the sense of L. Schwartz, and they are special representations of induced Kreǐn spaces. In this article we present a canonical representation of closely embedded Kreǐn spaces in terms of a generalization of the notion of operator range and obtain a characterization of uniqueness. When applied to Dirac operators, the results differ according to a mass or a massless particle in a dramatic way: in the case of a particle with a nontrivial mass we obtain a dual of a Sobolev type space and we have uniqueness, while in the case of a massless particle we obtain a dual of a homogenous Sobolev type space and we lose uniqueness. © 2010 Elsevier Inc.
Open Access
Kreǐn spaces induced by symmetric operators
(Academia Romana * Institutul de Matematica, 2009) Cojuhari P.; Gheondea, Aurelian
We introduce the notion of Kreǐn space induced by a densely defined symmetric operator in a Hilbert space, as an abstract notion of indefinite energy spaces. Characterizations of existence and uniqueness, as well as certain canonical representations, are obtained. We exemplify these by the free and certain perturbed Dirac operators.