We consider the difference f(−∆+V )−f(−∆) of functions of Schrödinger operators in L(R) and provide conditions under which this difference is trace class. We are particularly interested in non-smooth functions f and in V belonging only to some L space. This is motivated by applications in mathematical physics related to Lieb–Thirring inequalities. We show that in the particular case of Schrödin...

In an earlier paper 1] two of us studied generalized transfer operators M associated to maps of intervals of R. In particular the analyticity of a sharp determinant Det # (1?zM) was analyzed on the basis of spectral properties of M and by relating Det # (1 ? zM) to the determinant of 1 + D(z) for a suitable kneading operator D(z). It is a natural idea to try to replace monotone maps of interval...

A general procedure is derived for obtaining sufficient conditions for the similarity of operators T and T + P. This is applied to obtain sharp conditipns for the similarity of the Volterra operators J: f(x)-+ / f(y)dy and J + P where P: f(x) /+/fp(x,y)f(y)dy. By the same methods perturbations of the one sided shift operator S on LP(Ofo) by certain trace class operators P are shown to be simila...

In this paper the spectral properties of Dirac operators Aη with electrostatic δ-shell interactions of constant strength η supported on compact smooth surfaces in R3 are studied. Making use of boundary triple techniques a Krein type resolvent formula and a Birman-Schwinger principle are obtained. With the help of these tools some spectral, scattering, and asymptotic properties of Aη are investi...

Working within the framework of the covariant perturbation theory, we obtain the coincidence limit of the heat kernel of an elliptic second order differential operator that is applicable to a large class of quantum field theories. The basis of tensor invariants of the curvatures of a gravity and gauge field background, to the second order, is derived, and the form factors acting on them are obt...

Let be a C∗-algebra with identity 1, and let s( ) denote the set of all states on . For p,q,r ∈ [1,∞), denote by r( ) the set of all infinite matrices A= [ajk]j,k=1 over such that the matrix (φ[A[2]]) [r] := [(φ(ajkajk))]j,k=1 defines a bounded linear operator from p to q for all φ∈ s( ). Then r( ) is a Banach algebra with the Schur product operation and norm ‖A‖ = sup{‖(φ[A[2]])‖ : φ∈ s( )}. A...

We classify the operator content of local hermitian scalar operators in the SinhGordon model by means of independent solutions of the form-factor bootstrap equations. The corresponding linear space is organized into a tower-like structure of dimension n for the form factors F2n and F2n−1. Analyzing the cluster property of the form factors, a particular class of these solutions can be identified...

Let π denote the intractable posterior density that results when the standard default prior is placed on the parameters in a linear regression model with iid Laplace errors. We analyze the Markov chains underlying two different Markov chain Monte Carlo algorithms for exploring π. In particular, it is shown that the Markov operators associated with the data augmentation (DA) algorithm and a sand...

The paper studies the non-selfadjoint linear differential operator Ly = d dt ( (1−acos t)y+bsin t dy dt ) acting in the Hilbert space L2(−π,π) that originated from a steady state stability problem in fluid dynamics. The operator L is of Heun type and involves two parameters a,b related to the hydrostatic pressure and capillary properties of the fluid. The results concern (1) the properties of f...