Related papers: Spectral averaging for trace compatible operators
We study convergence of the spectral shift function for the finite interval restrictions of a pair of full-line Schr\"odinger operators to an interval of the form $(-\ell,\ell)$ with coupled boundary conditions at the endpoints as $\ell\to…
Spectral Barron spaces, which quantify the absolute value of weighted Fourier coefficients of a function, have gained considerable attention due to their capability for universal approximation across certain function classes. By…
This paper establishes trace-formulae for a class of operators defined in terms of the functional calculus for the Laplace operator on divergence-free vector fields with relative and absolute boundary conditions on Lipschitz domains in…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
We develop an analog of classical oscillation theory for Sturm-Liouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by…
We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the heat operator in a general semi-finite von Neumann algebra. Our results have several applications. We…
We give a definition of the spectral flow for paths of bounded essentially hyperbolic operators on a Banach space. The spectral flow induces a group homomorphism on the fundamental group of every connected component of the space of…
Inverse spectral problem for a self-adjoint differential operator, which is the sum of the operator of the third derivative on a finite interval and of the operator of multiplication by a real function (potential), is solved. Closed system…
We consider substitutions on compact alphabets and provide sufficient conditions for the diffraction to be pure point, absolutely continuous and singular continuous. This allows one to construct examples for which the Koopman operator on…
In the first section we provide a solution to the M. G. Krein problem about an inner description of the space $L_2(\Sigma,H).$ In the second section we introduce the multiplicity function for an operator measure. Making use of the…
A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…
We define the local trace function for subspaces of $\ltworn$ which are invariant under integer translation. Our trace function contains the dimension function and the spectral function defined by Bownik and Rzeszotnik and completely…
In this paper we develop the spectral theory of the fractional Brownian motion (fBm) using the ideas of Krein's work on continuous analogous of orthogonal polynomials on the unit circle. We exhibit the functions which are orthogonal with…
The in-in path integral of a scalar field propagating in a fixed background is formulated in a suitable function space. The free kinetic operator, whose inverse gives the propagators of the in-in perturbation theory, becomes essentially…
We prove some new pointwise-in-energy bounds on the expectations of various spectral shift functions associated with random Schr\"{o}dinger operators in the continuum having Anderson-type random potentials in both finite-volume and…
We study the relationship between the spectral shift function and the excess charge in potential scattering theory. Although these quantities are closely related to each other, they have been often formulated in different settings so far.…
We derive a formula for the regularized trace of operators with compact spectrum which act on the space of square integrable functions on the quotient of a semisimple Liegroup of real rank one by a convex-cocompact subgroup. The sum of…
In this paper, we study the spectrality of infinite convolutions in $\mathbb{R}^d$, where the spectrality means the corresponding square integrable function space admits a family of exponential functions as an orthonormal basis. Suppose…
Let G be the group GL(n) over a number field E and let A be the ring of adeles of E. In this paper we prove that the spectral side of the Arthur trace formula for G is absolutely convergent for all integrable rapidly decreasing functions on…
The Vafa-Witten equations (with or without a mass term) constitute a non-linear, first order system of differential equations on a given oriented, compact, Riemannian 4-manifold. Because these are the variational equations of a functional,…