We prove that the resolvent of renormalised Nelson Hamiltonian at fixed total momentum P improves positivity in (momentum) Fock-representation, for every P. Our argument is based on an explcit representation operator and its domain using interior boundary conditions.

The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space L (X,μ) and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of A and then using the Stieltjes inversion formula. 1. Preliminaries The set of generalized r...

A non-self-adjoint, rank-one Friedrichs model operator in L2(R) is considered in the case where the determinant of perturbation is an outer function in the half-planes C±. Its spectral structure is investigated. The impact of the linear resolvent growth condition on its spectral properties (including the similarity problem) is studied.

In this paper, by using the concept of the resolvent operator, we study the behavior and sensitivity analysis of the solution set for a new class of parametric generalized nonlinear implicit quasi-variational inclusion problem in Lp(p ≥ 2) spaces. The results presented in this paper are new and generalize many known results in this field.

In this expository paper, we discuss the use of the Evans function in finding resonances, which are poles of the analytic continuation of the resolvent. We illustrate the utility of the general theory developed in [13, 14] by applying it to two physically interesting test cases: the linear Schrödinger operator and the linearization associated with the integrable nonlinear Schrödinger equation.

In this paper, by using the concept of the resolvent operator, we study the behavior and sensitivity analysis of the solution set for a class of parametric generalized strongly nonlinear mixed quasivariational inclusion problem in Banach spaces. The results presented in this paper are new and generalize many known results in this field. Mathematics Subject Classification: 49J40, 90C20

Let A be a bounded linear operator on a Banach space such that the resolvent of A is rational. If 0 is in the spectrum of A, then it is well known that A is Drazin invertible. We investigate spectral properties of the Drazin inverse of A. For example we show that the Drazin inverse of A is a polynomial in A.

This work is concerned with the approximation to the solutions of the stochastic Stokes equations by the splitting up method. We apply the resolvent operator to evaluate the solution of the deterministic equations at the endpoints of every small interval, and the error is estimated.

In this paper, we consider the Lamé operator $$-\Delta ^*$$ and study resolvent estimate, uniform Sobolev Carleman estimate for . First, obtain sharp $$L^p$$ – $$L^q$$ estimates admissible p, q. This extends particular case $$q=\frac{p}{p-1}$$ due to Barceló et al. [4] Cossetti [8]. Secondly, show failure of For purpose directly analyze Fourier multiplier resolvent. allows us prove not only upp...

In this paper, we prove the existence of solutions for a class of nonlinear variational inclusion problems in semi-inner product spaces. We construct an iterative algorithm for approximating the solution for the class of variational inclusions involving A-monotone operators by using the resolvent operator technique.