Spectral theory of the Klein-Gordon equation in Pontryagin spaces

Langer, Heinz; Najman, Branko; Tretter, Christiane (2006). Spectral theory of the Klein-Gordon equation in Pontryagin spaces. Communications in mathematical physics, 267(1), pp. 159-180. Heidelberg: Springer 10.1007/s00220-006-0022-4

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In this paper we investigate an abstract Klein–Gordon equation by means of indefinite inner product methods. We show that, under certain assumptions on the potential which are more general than in previous works, the corresponding linear operator A is self-adjoint in the Pontryagin space K induced by the so-called energy inner product. The operator A possesses a spectral function with critical points, the essential spectrum of A is real with a gap around 0, and the non-real spectrum consists of at most finitely many pairs of complex conjugate eigenvalues of finite algebraic multiplicity; the number of these pairs is related to the ‘size’ of the potential. Moreover, A generates a group of bounded unitary operators in the Pontryagin space K. Finally, the conditions on the potential required in the paper are illustrated for the Klein–Gordon equation in Rn; they include potentials consisting of a Coulomb part and an L p -part with n ≤ p < ∞.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Tretter, Christiane

ISSN:

0010-3616

Publisher:

Springer

Language:

English

Submitter:

Factscience Import

Date Deposited:

04 Oct 2013 14:47

Last Modified:

05 Dec 2022 14:14

Publisher DOI:

10.1007/s00220-006-0022-4

Web of Science ID:

000239741700008

BORIS DOI:

10.48350/19391

URI:

https://boris.unibe.ch/id/eprint/19391 (FactScience: 1981)

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