Strauss, Y. Resonances in the rigged Hilbert space and Lax-Phillips scattering theory. (English) Zbl 1050.81066 Int. J. Theor. Phys. 42, No. 10, 2285-2315 (2003). 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 B. Sz.-Nagy and 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 [A. Bohm and 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. Reviewer: Eckhard Giere (Clausthal-Zellerfeld) Cited in 10 Documents MSC: 81U05 \(2\)-body potential quantum scattering theory 81U99 Quantum scattering theory 47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces 47A40 Scattering theory of linear operators 47N50 Applications of operator theory in the physical sciences 46E15 Banach spaces of continuous, differentiable or analytic functions 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:resonance; semigroup evolution; Lax-Philips scattering theory; rigged Hilbert space; Hardy space; Toeplitz operator Citations:Zbl 0201.45003; Zbl 0691.46051 PDFBibTeX XMLCite \textit{Y. Strauss}, Int. J. Theor. Phys. 42, No. 10, 2285--2315 (2003; Zbl 1050.81066)