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- Title
AN OPERATOR RICCATI EQUATION AND REFLECTIONLESS SCHR¨ODINGER OPERATORS.
- Authors
MYKYTYUK, YA. V.; SUSHCHYK, N. S.
- Abstract
In this paper, we study a connection between the operator Riccati equation S′(x) = KS(x) + S(x)K - 2S(x)KS(x), x ∈ R, and the set of reflectionless Schr¨odinger operators with operator-valued potentials. Here K ∈ B(H), K > 0 and S: R → B(H), where B(H) is the Banach algebra of all linear continuous operators acting in a separable Hilbert space H. Let S+(K) be the set of all solutions S of the Riccati equation satisfying the conditions 0 < S(0) < I and S′(0) ≥ 0, with I being the identity operator in H. We show that every solution S ∈ S+(K) generates a reflectionless Schr¨odinger operator with some potential q that is an analytic function in the strip...
- Subjects
RICCATI equation; SCHRODINGER operator; HILBERT space; ANALYTIC functions; OPERATOR-valued measures; BANACH algebras; LINEAR operators
- Publication
Matematychni Studii, 2024, Vol 61, Issue 2, p176
- ISSN
1027-4634
- Publication type
Article
- DOI
10.30970/ms.61.2.176-187