Related papers: Asymptotics of the Heat Kernel on Rank 1 Locally S…

We consider zeta functions and heat-kernel expansions on the bounded, generalized cone in arbitrary dimensions using an improved calculational technique. The specific case of a global monopole is analysed in detail and some restrictions…

The high temperature asymptotics of the Helmholtz free energy of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel…

We calculate a temperature dependent part of the one-loop thermodynamic potential (and the free energy) for charged massive fields in a general class of irreducible rank 1 symmetric spaces. Both low- and high-temperature expansions are…

We analyze the asymptotic behaviour of the heat kernel defined by a stochastically perturbed geodesic flow on the cotangent bundle of a Riemannian manifold for small time and small diffusion parameter. This extends WKB-type methods to a…

Let $X$ be a compact oriented CR manifold of dimension $2n+1$, $n \ge 1$, with a nondegenerate Levi form of constant signature $(n_-, n_+)$. Suppose that condition $Y(q)$ holds at each point of $X$, we establish the small time asymptotics…

By using ideas and strong results borrowed from the classical moment problem, we show how -under very general conditions- a discrete number of values of the spectral zeta function (associated generically with a non-decreasing sequence of…

We give sharp asymptotic estimates at infinity of all radial partial derivatives of the heat kernel on H-type groups. As an application, we give a new proof of the discreteness of the spectrum of some natural sub-Riemannian…

We explicitly construct a heat kernel as a Neumann series for certain function spaces, such as $L^{1}$, $L^{2}$, and Hilbert spaces, associated to a locally compact Hausdorff space $\mathfrak{X}$ with Borel $\sigma$-algebra $\mathcal{B}$,…

In this paper, we study the asymptotic behavior of the heat kernel with respect to the Witten Laplacian. We introduce the localization and the scaling technique in semi-classical analysis, and study the semi-classical asymptotic behavior of…

In this paper we investigate the small time heat kernel asymptotics on the cut locus on a class of surfaces of revolution, which are the simplest 2-dimensional Riemannian manifolds different from the sphere with non trivial cut-conjugate…

We suggest a method of reduction of mixed absolute and relative boundary conditions to pure ones. The case of rank two tensor is studied in detail. For four-dimensional disk the corresponding heat kernel is expressed in terms of scalar heat…

Spectral functions relevant in the context of quantum field theory under the influence of spherically symmetric external conditions are analysed. Examples comprise heat-kernels, determinants and spectral sums needed for the analysis of…

We consider Dirichlet heat kernel $p_a^{(\mu)}(t,x,y)$ for the Bessel differential operator $L^{(\mu)}=\frac{d^2}{dx^2}+\frac{2\mu+1}{2x}$, $\mu\in\mathbb{R}$, in half-line $(a,\infty)$, $a>0$, and provide its asymptotic expansions for…

We establish small-time asymptotic expansions for heat kernels of hypoelliptic H\"ormander operators in a neighborhood of the diagonal, generalizing former results obtained in particular by M\'etivier and by Ben Arous. The coefficients of…

I discuss the trace of a heat kernel Tr[e^(-tA)] for compact fuzzy spaces. In continuum theory its asymptotic expansion for t -> +0 provides geometric quantities, and therefore may be used to extract effective geometric quantities for fuzzy…

For a given spectrum {lambda_{n}} of the Laplace operator on a Riemannian manifold, in this paper, we present a relation between the counting function N(lambda), the number of eigenvalues (with multiplicity) smaller than \lambda, and the…

We compute the full asymptotic expansion of the heat kernel Trace$(\exp(-tD^2))$ where $D$ is, assuming RH, the self-adjoint operator whose spectrum is formed of the imaginary parts of non-trivial zeros of the Riemann zeta function. The…

For parabolic spatially discrete equations, we consider Green's functions, also known as heat kernels on lattices. We obtain their asymptotic expansions with respect to powers of time variable $t$ up to an arbitrary order and estimate the…

For a class of Laplace exponents we derive the heat trace asymptotics of the generator of the corresponding subordinate Brownian motion on Euclidean space. The terms in the asymptotic expansion are found to depend both on the geometry of…

By adapting a technique of Molchanov, we obtain the heat kernel asymptotics at the sub-Riemannian cut locus, when the cut points are reached by an $r$-dimensional parametric family of optimal geodesics. We apply these results to the…