Related papers: The Heat Kernel Coefficients to the Matrix Schr\"o…
We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are H\"older continuous locally in space and time. This is done via local…
In this article we give explicit solutions for the wave equations associated to the modified Schr\"odinger operators with magnetic field on the disc and the upper half plane models of the hyperbolic plane. We show that the modified…
The heat kernel on the symmetric space of positive definite Hermitian matrices is used to endow the spaces of Bergman metrics of degree k on a Riemann surface M with a family of probability measures depending on a choice of the background…
We derive several properties of the heat equation with the Hodge operator associated with the Rumin complex on Heisenberg groups and prove several properties of the fundamental solution. As an application, we use the heat kernel for Rumin's…
We study computational problems related to the Schr\"odinger operator $H = -\Delta + V$ in the real space under the condition that (i) the potential function $V$ is smooth and has its value and derivative bounded within some polynomial of…
We present a very quick and powerful method for the calculation of heat-kernel coefficients. It makes use of rather common ideas, as integral representations of the spectral sum, Mellin transforms, non-trivial commutation of series and…
We propose an efficient regularization method for functional determinants of radial operators using heat kernel coefficients. Our key finding is a systematic way to identify heat kernel coefficients in the angular momentum space. We…
We construct an index of first-order, self-adjoint, elliptic differential operators in the $K$-theory of a Fr\'echet algebra of smooth kernels with faster than exponential off-diagonal decay. We show that this index can be represented by an…
This paper establishes by employing analytic and probabilistic techniques estimates concerning the {\it heat content} for the fractional Schr\"odinger operator $\F+\ind$ with $0<\alpha\leq 2$ in $\Rd$, $d\geq 2$ and $\dom$ a Lebesgue…
We compute the heat kernel coefficients that are needed for the regularization and renormalization of massive gravity. Starting from the Stueckelberg action for massive gravity, we determine the propagators of the different fields (massive…
The purpose of this article is to establish regularity and pointwise upper bounds for the (relative) fundamental solution of the heat equation associated to the weighted dbar-operator in $L^2(C^n)$ for a certain class of weights. The…
In this paper we propose a generalization of the Gilkey-de Witt heat kernel expansion, designed to provide us with a precise estimation of the heat trace of non-negative Schroedinger type differential operators with non-trivial kernel over…
Schr\"odinger operators with periodic (possibly complex-valued) potentials and discrete periodic operators (possibly with complex-valued entries) are considered, and in both cases the computational spectral problem is investigated: namely,…
We prove a sharp H\"ormander multiplier theorem for Schr\"odinger operators $H=-\Delta+V$ on $\mathbb{R}^n$. The result is obtained under certain condition on a weighted $L^\infty$ estimate, coupled with a weighted $L^2$ estimate for $H$,…
We calculate the heat-kernel coefficients, up to $a_2$, for a U(1) bundle on the 4-Ball for boundary conditions which are such that the normal derivative of the field at the boundary is related to a first-order operator in boundary…
We build a systematic calculational method for the covariant expansion of the two-point heat kernel $\hat K(\tau|x,x')$ for generic minimal and non-minimal differential operators of any order. This is the expansion in powers of dimensional…
A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.
The heat kernel in curved space-time is computed to fourth order in a strict expansion in the number of covariant derivatives. The computation is made for arbitrary non abelian gauge and scalar fields and for the Riemann connection in the…
We consider the heat semi-group generated by the Laplace operator on metric trees. Among our results we show how the behavior of the associated heat kernel depends on the geometry of the tree. As applications we establish new eigenvalue…
We survey the recent progress in the study of heat kernels for a class of non-symmetric non-local operators. We focus on the existence and sharp two-sided estimates of the heat kernels and their connection to jump diffusions.