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- W163321459 abstract "A partial non-stationary perturbation determinant Δ1 (t) is defined as follows: $$begin{array}{*{20}{c}} {{Delta _1}(t): = det left( {{e^{itA}}{P_1}{e^{ - itH}}{|_{{mathcal{H}_1}}}} right),}&{t > 0;} end{array}$$here A is a self-adjoint operator in some Hilbert space ({mathcal{H}_1}), H is a self-adjoint operator in a larger Hilbert space (mathcal{H} supset {mathcal{H}_1}), P 1 i the orthogonal projection in (mathcal{H}) onto ({mathcal{H}_1}) and ({P_1}(H - A){|_{{mathcal{H}_1}}}) is a trace class operator in ({mathcal{H}_1}). If the operator P 1 H(I- P 1) is finite-dimensional, Δ1(t) is expressed by the resolvent kernel of a system of Fredholm integral equations on (0, t) of second kind. Moreover, in a particular situation the asymtotic behavior of Δ1(t) for t → ∞ is studied." @default.
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- W163321459 date "2004-01-01" @default.
- W163321459 modified "2023-10-03" @default.
- W163321459 title "Partial Non-stationary Perturbation Determinants" @default.
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- W163321459 doi "https://doi.org/10.1007/978-3-0348-7947-7_1" @default.
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