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• W1600794395 abstract "We discuss the connection between Lax—Phillips scattering theory and the theory of well-posed linear systems, and show that the latter theory is a natural extension of the former. As a consequence of this, there is a close connection between the Lax—Phillips generator and the generators of the corresponding well-posed linear system. All the essential information about these two systems is contained in the system operator $${{S}_{sum }} = left[ {begin{array}{*{20}{c}} {A B} {C & D} end{array} } right]$$ , where A is the generator of the (central) semigroup, B is the control operator, and C&D is the combined observation/feedthrough operator. In the important Hilbert space case this system operator can be written in the more familiar form $$ {{S}_{sum }} = left[ {frac{{A B}}{{C D}}} right] $$ , where $$bar C $$ is a (not necessarily uniquely determined) observation operator and D is the corresponding (generalized) feedthrough operator. The system operator is closed and densely defined. In the reflexive case the adjoint of S Σ is the system operator of the dual system. We give formulas for the Lax-Phillips generator and resolvent in terms of the system operator. By applying the Hille—Yoshida theorem to the Lax—Phillips semigroup we get necessary and sufficient conditions for the L p -admissibility or joint L p -admissibility of a control operator B and an observation operator C. This leads to a criterion for an H ∞-function to be an L p -multiplier." @default.
• W1600794395 created "2016-06-24" @default.
• W1600794395 creator A5062257326 @default.
• W1600794395 date "2001-01-01" @default.
• W1600794395 modified "2023-10-14" @default.
• W1600794395 title "Well-Posed Linear Systems, Lax-Phillips Scattering, and L p -Multipliers" @default.
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• W1600794395 doi "https://doi.org/10.1007/978-3-0348-8362-7_18" @default.
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