Accretive and sectorial extensions of nonnegative symmetric operators (Q371700)

\textit{J. von Neumann} in his famous article [Math. Ann. 102, 49--131 (1929; JFM 55.0824.02)] created a theory of self-adjoint extensions of a given symmetric operator on some Hilbert space. \textit{M. Krein} [Mat. Sb., N. Ser. 20(62), 431--495 (1947; Zbl 0029.14103)] gave a description of all nonnegative self-adjoint extensions of a nonnegative symmetric operator (here, of course, we should also mention the works of M. Vishik and M. Birman). In connection with the study of hyperbolic equations, \textit{R. S. Phillips} [Trans. Am. Math. Soc. 90, 193--254 (1959; Zbl 0093.10001)] posed the problem about description and parametrization of all maximal accretive extensions of a densely defined non-negative operator. The paper under review contains the solution to the Phillips problem for maximal accretive and sectorial quasi-self-adjoint extensions \(\widetilde{S}(S \subset \widetilde{S} \subset S^*\)) of a closed, densely defined nonnegative operator \(S\) in some Hilbert space. This description and parametrization are presented in terms of some sort of an analogy of von Neumann's formulas for quasi-self-adjoint extensions. An application to operators corresponding to finite number \(\delta^\prime\)-interactions on the real line is given as well as to the parametrization of all resolvents of maximal accretive extensions.