Related papers: Trace expansions for elliptic cone operators with …
We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the…
We study the closed extensions (realizations) of differential operators subject to homogeneous boundary conditions on weighted L_p-Sobolev spaces over a manifold with boundary and conical singularities. Under natural ellipticity conditions…
Our goal is to extend the theory of the spectral shift function to the case where only the difference of some powers of the resolvents of self-adjoint operators belongs to the trace class. As an example, we consider a couple of Dirac…
In this paper we provide a complete study of the spectrum of a constant coefficients differential operator on a scale of localized Sobolev spaces, $H^{s}_{loc}(I),$ which are Fr\'echet spaces. This is quite different from what we find in…
The spectral theory of the Laplace differential operator for biregular quantum graphs is developed. Trees are studied in detail. Generating functions for closed non backtracking walks appear when resolvents for trees are related to…
We consider a general second-order elliptic differential operator on a domain with a cylindrical end. We impose Dirichlet boundary conditions on the boundary with the exception of a small set, where we impose Neumann boundary conditions.…
We consider various closed (and self-adjoint) extensions of elliptic differential expressions of the type $\cA=\sum_{0\le |\alpha|,|\beta|\le m}(-1)^\alpha D^\alpha a_{\alpha, \beta}(x)D^\beta$, $a_{\alpha, \beta}(\cdot)\in…
We derive a detailed asymptotic expansion of the heat trace for the Laplace-Beltrami operator on functions on manifolds with conic singularities, using the Singular Asymptotics Lemma of Jochen Bruening and Robert T. Seeley [BS]. In the…
In three-dimensional case, we consider two classical operators: Schrodinger operator and an operator in the divergence form. For slowly-decaying oscillating potentials, we establish spatial asymptotics of the Green's function. The main term…
We provide conditions under which trajectory outcomes in mechanical systems subject to unilateral constraints depend piecewise-differentiably on initial conditions, even as the sequence of constraint activations and deactivations varies.…
It is a well-known fact that the first and last non-trivial coefficients of the characteristic polynomial of a linear operator are respectively its trace and its determinant. This work shows how to compute recursively all the coefficients…
This paper deals with the study of the two-dimensional Dirac operatorwith infinite mass boundary condition in a sector. We investigate the question ofself-adjointness depending on the aperture of the sector: when the sector is convexit is…
In the field of enumeration of walks in cones, it is known how to compute asymptotically the number of excursions (finite paths in the cone with fixed length, starting and ending points, using jumps from a given step set). As it turns out,…
We continue the analysis of the elliptic part of the trace formula initiated in \cite{Altug:2015aa}. In that reference Poisson summation was applied to the elliptic part and the dominant term was analyzed. The main aim of this paper is to…
It is shown that a valuation of residue characteristic different from $2$ and $3$ on a field $E$ has at most one extension to the function field of an elliptic curve over $E$, for which the residue field extension is transcendental but not…
We study the existence of uniformly bounded extension and trace operators for W^{1,p}-functions on randomly perforated domains, where the geometry is assumed to be stationary ergodic. Such extension and trace operators are important for…
We develop a sharp boundary trace theory in arbitrary bounded Lipschitz domains which, in contrast to classical results, allows "forbidden" endpoints and permits the consideration of functions exhibiting very limited regularity. This is…
In this paper, we show that the trace of the operators $A\eta(t\mathcal{L})$ where $A$ and $\mathcal {L}$ are classical pseudo-differential operators on a compact manifold $M$ and $\mathcal {L}$ is elliptic and self-adjoint admits an…
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…
This paper is concerned with investigating the asymptotic behavior of the gradients of solutions to a class of elliptic systems with general boundary data, especially covering the Lam\'{e} systems, in a narrow region. The novelty of this…