Related papers: A new algebraic approach for calculating the heat …

We derive symmetric and antisymmetric kernels by symmetrizing and antisymmetrizing conventional kernels and analyze their properties. In particular, we compute the feature space dimensions of the resulting polynomial kernels, prove that the…

In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann cap) subjected to Dirichlet boundary conditions. By…

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…

We construct the covariant effective field theory of gravity as an expansion in inverse powers of the Planck mass, identifying the leading and next-to-leading quantum corrections. We determine the form of the effective action for the cases…

We prove upper and lower bounds of the heat kernel for the operator $\Delta-\nabla (\frac{1}{|x|^{\alpha}})\cdot \nabla $ in $\mathbb{R}^{n}\setminus\{0} $ where $\alpha >0$. We obtain these bounds from an isoperimetric inequality for a…

Let $G$ be a compact connected Lie group equipped with a bi-invariant metric. We calculate the asymptotic expansion of the heat kernel of the laplacian on $G$ and the heat trace using Lie algebra methods. The Duflo isomorphism plays a key…

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…

A special class of non-minimal operators which are relevant for quantum field theory is introduced. The general form of the heat kernel coefficients of these operators on manifolds without boundary is described. New results are presented…

Let $\Delta$ be the Laplace--Beltrami operator acting on a non-doubling manifold with two ends $\mathbb R^m \sharp \mathcal R^n$ with $m > n \ge 3$. Let $\frak{h}_t(x,y)$ be the kernels of the semigroup $e^{-t\Delta}$ generated by $\Delta$.…

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…

Standard thermodynamic treatments of quantum field theory in the presence of black-hole backgrounds reproduce the black hole entropy by usually specializing to the leading order of the heat-kernel or the high-temperature expansion. By…

A key problem in the attempt to quantize the gravitational field is the choice of boundary conditions. These are mixed, in that spatial and normal components of metric perturbations obey different sets of boundary conditions. In the…

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the…

In this work we construct the heat kernel of the 1/2-order Laplacian perturbed by the first-order gradient term in H\"older space and the zero-order potential term in generalized Kato's class, and obtain sharp two-sided estimates as well as…

We consider the asymptotic expansion of the heat kernel of a generalized Laplacian for $t\to 0^+$ and characterize the coefficients $a_k$ of this expansion by a natural intertwining property. In particular we will give a closed formula for…

We obtain sharp two-sided heat kernel estimates on spaces with varying dimension, in which two spaces of general dimension are connected at one point. On these spaces, if the dimensions of the two constituent parts are different, the volume…

An asymptotic expansion of the trace of the heat kernel on a cone where the heat coefficients have a delta function behavior at the apex is obtained. It is used to derive the renormalized effective action and total energy of a…

We establish a Gaussian upper bound of the heat kernel for the Laplace-Beltrami operator on complete Riemannian manifolds with Bakry-\'Emery Ricci curvature bounded below. As applications, we first prove an L^1-Liouville property for…

A non-relativistic quantum model is considered with a point particle carrying a charge $e$ and moving on the plane pierced by two infinitesimally thin Aharonov-Bohm solenoids and subjected to a perpendicular uniform magnetic field of…

Using the technique of labeled operators, compact explicit expressions are given for all traced heat kernel coefficients containing zero, two, four and six covariant derivatives, and for diagonal coefficients with zero, two and four…