Abstract:
A functional model is constructed for the Lie algebra ISO(1,1) of linear non-self-adjoint operators subject to the commutation relations [A1,A2]=0, [A1,A3]=iA2, [A2,A3]=iA1. The construction is based on a non-Abelian generalization of the Lax–Phillips scattering scheme on the group of transformations of the pseudo-Euclidean plane preserving the quadratic form x2−y2.
\Bibitem{Zol95}
\by V.~A.~Zolotarev
\paper A functional model for the~Lie algebra $\operatorname{ISO}(1,1)$ of linear non-self-adjoint operators
\jour Sb. Math.
\yr 1995
\vol 186
\issue 1
\pages 79--106
\mathnet{http://mi.mathnet.ru/eng/sm5}
\crossref{https://doi.org/10.1070/SM1995v186n01ABEH000005}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1641676}
\zmath{https://zbmath.org/?q=an:0854.47006}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995RZ91900005}
Linking options:
https://www.mathnet.ru/eng/sm5
https://doi.org/10.1070/SM1995v186n01ABEH000005
https://www.mathnet.ru/eng/sm/v186/i1/p79
This publication is cited in the following 4 articles:
V.A. Zolotarev, Analytic Methods of Spectral Representations of Non- Selfadjoint (Non-Unitary) Operators, 2020
Zolotarev V., “A Functional Model for the Lie Algebra Sl(2, R) of Linear Non-Self-Adjoint Operators”, Operator Theory, System Theory and Related Topics: the Moshe Livsic Anniversary Volume, Operator Theory : Advances and Applications, 123, ed. Alpay D. Vinnikov V., Birkhauser Verlag Ag, 2001, 539–567
V. A. Zolotarev, Operator Theory, System Theory and Related Topics, 2001, 539
Zolotarev V., “Functional Models for Algebras of Linear Nonselfadjoint Operators”, Z. Angew. Math. Mech., 77:2 (1997), S695–S696
Citation in format AMSBIB
Contact us: