The inverse decay problem

L. P. Horwitz; J. A. LaVita; J. P. Marchand

doi:10.1063/1.1665570

The inverse decay problem

L. P. Horwitz, J. A. LaVita, J. P. Marchand

University of Denver

Research output: Contribution to journal › Article › peer-review

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Abstract

Let U_{script K}(t) be a one-parameter operator family of positive type in a Hilbert space script K and U(t) its minimal unitary dilation with infinitesimal generator H. If U_{script K}(t) is a contractive semigroup, then H is not positive. If in addition U_{script K}(t)→0 for t→∞, then there exists a state φ ∈ script K on which H is not defined. We interpret these and other results in the context of the quantum-mechanical theory of unstable particles and the scattering theory of Lax and Phillips.

Original language	English
Pages (from-to)	2537-2543
Number of pages	7
Journal	Journal of Mathematical Physics
Volume	12
Issue number	12
DOIs	https://doi.org/10.1063/1.1665570
State	Published - 1971
Externally published	Yes

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The inverse decay problem

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