Related papers: Regularized trace formula of magic Gribov operator…

We study operators defined on a Hilbert space defined by a self-affine Delone set $\Lambda$ and show that the usual trace of a restriction of the operator to finite-dimensional subspaces satisfies a certain $\limsup$ law controlled by…

In this paper we establish a T1 criterion for the boundedness of Hermite-Calderon-Zygmund operators on the BMO_H(R^n) space naturally associated to the Hermite operator H. We apply this criterion in a systematic way to prove the boundedness…

We prove the renormalizability to all orders of a refined Gribov-Zwanziger type action in linear covariant gauges in four-dimensional Euclidean space. In this model, the Gribov copies are taken into account by requiring that the…

In this paper, we study the change of spectrum and the existence of Riesz bases of specific classes of $n\times n$ unbounded operator matrices, called: diagonally and off-diagonally generalized subordinate block operator matrices. An…

This article is a continuation of our work on generalized matrix-weighted Besov--Triebel--Lizorkin-type spaces with matrix $\mathcal{A}_{\infty}$ weights. In this article, we establish the boundedness of pseudo-differential, trace, and…

Formulae expressing the trace of the composition of several (up to five) adjoint actions of elements of the Griess algebra of a vertex operator algebra are derived under certain assumptions on the action of the automorphism group. They…

This paper is a sequel to our earlier work [BFPRW], where we study the derived representation scheme DRep_{g}(A) parametrizing the representations of a Lie algebra A in a finite-dimensional reductive Lie algebra g. In [BFPRW], we defined…

We study integral operators on the space of square-integrable functions from a compact set, $X$, to a separable Hilbert space, $H$. The kernel of such an operator takes values in the ideal of Hilbert-Schmidt operators on $H$. We establish…

We obtain a trace formula for algebraic differential operators which the corresponding analytic results have been proved by M. Engeli and G. Felder

We present here simple trace formulas for Hecke operators $T_k(p)$ for all $p>3$ on $S_k(\Gamma_0(3))$ and $S_k(\Gamma_0(9))$, the spaces of cusp forms of weight $k$ and levels 3 and 9. These formulas can be expressed in terms of special…

We obtain a new simple formula for the regularized traces of singular ordinary differential operators.

Koplienko \cite{Ko} found a trace formula for perturbations of self-adjoint operators by operators of Hilbert-Schmidt class $\mathcal{B}_2(\mathcal{H})$. Later, Neidhardt introduced a similar formula in the case of pair of unitaries…

We compute the Dixmier trace of pseudo-Toeplitz operators on the Fock space. As an application we find a formula for the Dixmier trace of the product of commutators of Toeplitz operators on the Hardy and weighted Bergman spaces on the unit…

Let $H, V$ be self-adjoint operators such that $V$ belongs to the weak trace class ideal. We prove higher order perturbation formula $$\tau\big(f(H+V)-\sum_{j=0}^{n-1}\frac{1}{j!}\frac{d^j}{dt^j} f(H+tV)\big|_{t=0}\big)=\int_{\mathbb{R}}…

We consider the one dimensional Schr\"odinger operator with properly connecting generalized point interaction at the origin. We derive a trace formula for trace of difference of resolvents of perturbed and unperturbed Schr\"odinger…

In Communications in Mathematical Physics, no. 199, (1998), we have considered the Heun operator $\displaystyle{ H = a^* (a + a^*)a}$ acting on Bargmann space where $a$ and $a^{*}$ are the standard Bose annihilation and creation operators…

In this paper, we extend the class of admissible functions for the trace formula of the second order in the self-adjoint, unitary, and contraction cases for a perturbation in the Hilbert-Schmidt class $\mathcal{S}^2(\mathcal{H})$ by…

An exact trace formula for the perturbation of the Laplacian by a Dirac delta potential on a compact hyperbolic Riemann surface is derived. The formula can be considered an analogue of the Selberg trace formula. The difference of perturbed…

In this note we present the metric approximation property for weighted mixed-norm $L_w^{(p_1,\dots ,p_n)}$ and variable exponent Lebesgue type spaces. As a consequence, this also implies the same property for modulation and Wiener-Amalgam…

In the setting of a non-complete doubling metric measure space $(\Omega,d,\mu)$, we construct various bounded linear trace and extension operators for homogeneous and inhomogeneous Besov spaces $B^\alpha_{p,q}$. Equipping the boundary…