Initial value problems and Weyl-Titchmarsh theory for Schrödinger operators with operator-valued potentials. (English) Zbl 1283.34023

Gesztesy, Fritz; Weikard, R.; Zinchenko, Maxim

Oper. Matrices 7, No. 2, 241-283 (2013).

The principal purpose of this paper is to derive a streamlined version of the Weyl-Titchmarsh theory for Schrödinger operators on a finite or infinite interval with operator-valued potentials.
The results of the paper are new and interesting. The paper is well written and gives a contribution to the theory for differential operators with operator-valued potentials.

Reviewer: Chuan-Fu Yang (Nanjing)

MSC:

34B20	Weyl theory and its generalizations for ordinary differential equations
34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34B24	Sturm-Liouville theory
47E05	General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)

Keywords:

Weyl-Titchmarsh theory; ordinary differential equations with operator coefficients; Schrödinger operator