Related papers: Asymptotic expansions for trace functionals

In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.

Let $V$ be a vector space over a field $\mathbb F$ with scalar product given by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. If $\mathbb F=\mathbb C$, then we give canonical matrices of isometric and selfadjoint…

In this paper, we establish a generalized Taylor expansion of a given function $f$ in the form $\displaystyle{f(x) = \sum_{j=0}^m c_j^{\alpha,\rho}\left(x^\rho-a^\rho\right)^{j\alpha} + e_m(x)}$ \noindent with $m\in \mathbb{N}$,…

Given a complex, separable Hilbert space $\cH$, we consider differential expressions of the type $\tau = - (d^2/dx^2) + V(x)$, with $x \in (a,\infty)$ or $x \in \bbR$. Here $V$ denotes a bounded operator-valued potential $V(\cdot) \in…

We investigate minimal operator corresponding to operator differential expression with exit from space, study its selfadjoint extensions, also for one particular selfadjoint extension corresponding to boundary value problem with some…

We consider non-smooth functions of (truncated) Wiener--Hopf type operators on the Hilbert space $L^2(\mathbb R^d)$. Our main results are uniform estimates for trace norms ($d\ge 1$) and quasiclassical asymptotic formulas for traces of the…

By combining the Malliavin calculus with Fourier techniques, we develop a high-order asymptotic expansion theory for a sequence of vector-valued random variables. Our asymptotic expansion formulas give the development of the characteristic…

Given two linear operators $S$ and $T$ acting between Hilbert spaces $\mathscr{H}$ and $\mathscr{K}$, respectively $\mathscr{K}$ and $\mathscr{H}$ which satisfy the relation \begin{equation*} \langle Sh, k\rangle=\langle h, Tk\rangle, \quad…

A new technique for approximating eigenvalues and eigenvectors of a self-adjoint operator is presented. The method does not incur spectral pollution, uses trial spaces from the form domain, has a self-adjoint algorithm, and exhibits…

We formulate the issue of minimality of self-adjoint operators on a Hilbert space as a semi-definite problem, linking the work by Overton in [1] to the characterization of minimal hermitian matrices. This motivates us to investigate the…

Let F be the quotient of an analytic function with a product of linear functions. Working in the framework of analytic combinatorics in several variables, we compute asymptotic formulae for the Taylor coefficients of F using multivariate…

A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…

The purpose of this paper is to study nonnegative self-adjoint extensions associated with singular Sturm-Liouville expressions with strictly positive minimal operators. We provide a full characterization of all possible nonnegative…

A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-selfadjoint compact operator is given. Sufficient…

Using simple commutator relations, we obtain several trace identities involving eigenvalues and eigenfunctions of an abstract self-adjoint operator acting in a Hilbert space. Applications involve abstract universal estimates for the…

The abstract theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic operator on $\mathbb{R}^{n}$ with linear boundary conditions on (a relatively open part of) a…

Let Lf(x)=-\Delta f(x) + V(x)f(x), V\geq 0, V\in L^1_{loc}(R^d), be a non-negative self-adjoint Schr\"odinger operator on R^d. We say that an L^1-function f belongs to the Hardy space H^1_L if the maximal function M_L f(x)=\sup_{t>0}…

We consider a 3-dimensional Dirac operator H_0 with non-constant magnetic field of constant direction, perturbed by a sign-definite matrix-valued potential V decaying fast enough at infinity. Then we determine asymptotics, as the energy…

Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For operators $T$ with at least two points in their…

Consider a quasi-periodic Schr\"odinger operator $H_{\alpha,\theta}$ with analytic potential and irrational frequency $\alpha$. Given any rational approximating $\alpha$, let $S_+$ and $S_-$ denote the union, respectively, the intersection…