Resonances in the Rigged Hilbert Space and Lax-Phillips Scattering Theory
Copyright policy )Resonances in the Rigged Hilbert Space and Lax-Phillips Scattering Theory
The aim of the article is to uncover certain relations between the Lax-Phillips scattering theory, developed originally for acoustic or electromagnetic systems, and the rigged Hilbert space formalism. To this end the essentials of the Lax-Phillips scattering theory are presented in order to put the theory in a more general framework. The construction fits into the theory of \textit{B. Sz.-Nagy} and \textit{C. Foias} [Harmonic analysis of operators on Hilbert spaces. Amsterdam: North-Holland (1970; Zbl 0201.45003)] on contraction operators in Hilbert spaces. The last section is devoted to the development of a rigged Hilbert space formalism for resonances in the framework of the Lax-Phillips scattering theory. Considering operators of the form \(H = H_{0} +V\) the assumptions on the spectrum of \(H\) given in [\textit{A. Bohm} and \textit{M. Gadella}, Dirac kets, Gamov vectors and Gel'fand triplets. Berlin: Springer (1989; Zbl 0691.46051)] are imposed here as well. Additional assumptions are made in order to be able to use the theory of Hardy spaces.
- Tel Aviv University Israel
- University of Toronto Canada
\(2\)-body potential quantum scattering theory, Scattering theory of linear operators, Applications of operator theory in the physical sciences, Lax-Philips scattering theory, Quantum scattering theory, Hardy space, resonance, Toeplitz operator, rigged Hilbert space, Banach spaces of continuous, differentiable or analytic functions, semigroup evolution, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
\(2\)-body potential quantum scattering theory, Scattering theory of linear operators, Applications of operator theory in the physical sciences, Lax-Philips scattering theory, Quantum scattering theory, Hardy space, resonance, Toeplitz operator, rigged Hilbert space, Banach spaces of continuous, differentiable or analytic functions, semigroup evolution, (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).15 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!