Boundary values of resolvents of self-adjoint operators in Krein spaces
نویسنده
چکیده
We prove in this paper resolvent estimates for the boundary values of resolvents of selfadjoint operators on a Krein space: if H is a selfadjoint operator on a Krein space H, equipped with the Krein scalar product 〈·|·〉, A is the generator of a C0−group on H and I ⊂ R is an interval such that: 1) H admits a Borel functional calculus on I, 2) the spectral projection 1lI (H) is positive in the Krein sense, 3) the following positive commutator estimate holds: Re〈u|[H, iA]u〉 ≥ c〈u|u〉, u ∈ Ran1lI(H), c > 0. then assuming some smoothness of H with respect to the group eitA, the following resolvent estimates hold: sup z∈I±i]0,ν] ‖〈A〉(H − z)〈A〉‖ < ∞, s > 1 2 . As an application we consider abstract Klein-Gordon equations ∂ t φ(t) − 2ikφ(t) + hφ(t) = 0, and obtain resolvent estimates for their generators in charge spaces of Cauchy data.
منابع مشابه
AbstractAbstr GRAPH SUBSPACES AND THE SPECTRAL SHIFT FUNCTION
We extend the concept of Lifshits–Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of (admissible) operators that are similar to self-adjoint operators. An operator H is called admissible if: (i) there is a bounded operator V with a bounded inverse such that H = V −1 HV for some self-adjoint operator H; (ii) the operators H and H are resolvent ...
متن کاملError bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert spaces via a Taylor's type expansion
On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.
متن کاملComplex Symplectic Spaces and Boundary Value Problems
This paper presents a review and summary of recent research on the boundary value problems for linear ordinary and partial differential equations, with special attention to the investigations of the current authors emphasizing the applications of complex symplectic spaces. In the first part of the previous century, Stone and von Neumann formulated the theory of self-adjoint extensions of symmet...
متن کاملSturm–liouville Operators with Measure-valued Coefficients
We give a comprehensive treatment of Sturm–Liouville operators whose coefficients are measures including a full discussion of self-adjoint extensions and boundary conditions, resolvents, and Weyl–Titchmarsh–Kodaira theory. We avoid previous technical restrictions and, at the same time, extend all results to a larger class of operators. Our operators include classical Sturm– Liouville operators,...
متن کاملResolvents of self-adjoint extensions with mixed boundary conditions
We prove a variant of Krein’s resolvent formula for self-adjoint extensions given by arbitrary boundary conditions. A parametrization of all such extensions is suggested with the help of two bounded operators instead of multivalued operators and selfadjoint linear relations.
متن کامل