Related papers: Heat kernel expansion: user's manual
We propose a novel derivation of the non-local heat kernel expansion, first studied by Barvinsky, Vilkovisky and Avramidi, based on simple diagrammatic equations satisfied by the heat kernel. For Laplace-type differential operators we…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
We work out the general features of perturbative field theory on noncommutative manifolds defined by isospectral deformation. These (in general curved) `quantum spaces', generalizing Moyal planes and noncommutative tori, are constructed…
In previous works, we used a so-called deformation formula in order to study, in particular, the Borel summability of the heat kernel of some operators. A goal of this paper is to collect miscellaneous remarks related to these works. Here…
We prove sharp estimates of the heat kernel associated with Fourier-Dini expansions on $(0,1)$ equipped with Lebesgue measure and the Neumann condition imposed on the right endpoint. Then we give several applications of this result…
The conformal powers of the Laplacian of a Riemannian metric which are known as the GJMS-operators admit a combinatorial description in terms of the Taylor coefficients of a natural second-order one-parameter family $\H(r;g)$ of…
This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and…
We study an index of a transversal Dirac operator on an odd-dimensional manifold $X$ with locally free $\mathbb{S}^1$-action. One difficulty of using heat kernel method lies in the understanding of the asymptotic expansion as $t\to 0^+$. By…
Wavelet bases and frames consisting of band limited functions of nearly exponential localization on Rd are a powerful tool in harmonic analysis by making various spaces of functions and distributions more accessible for study and…
We study the heat kernel for the Laplace type partial differential operator acting on smooth sections of a complex spin-tensor bundle over a generic $n$-dimensional Riemannian manifold. Assuming that the curvature of the U(1) connection…
In this paper, we introduce heat kernel coupling (HKC) as a method of constructing multimodal spectral geometry on weighted graphs of different size without vertex-wise bijective correspondence. We show that Laplacian averaging can be…
Let $G$ be a noncompact semisimple Lie group equipped with a certain invariant Riemannian metric. Then, we can consider a heat kernel function on $G$ associated to the Riemannian metric. We give an explicit formula for the heat kernel when…
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…
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…
In this paper, we present an explicit description for the boundary behavior of the Bergman kernel function, the Bergman metric, and the associated curvatures along certain sequences converging to an $h$-extendible boundary point.
Let us consider a time-dependent differential operator quadratic with respect to the phase variables. Let us consider a multiplication operator defined with the help of a "small" matrix-valued function. Under suitable conditions, we give an…
Among those transversally elliptic operators initiated by Atiyah and Singer, Kohn's $\Box_b$ operator on CR manifolds with $S^1$ action is a natural one of geometric significance for complex analysts. Our first main result establishes an…
We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating…
Thermal expansion in materials can be accurately modeled with careful anharmonic phonon calculations within density functional theory. However, because of interest in controlling thermal expansion and the time consumed evaluating thermal…
We construct the biharmonic heat kernel for a suitable self-adjoint extension of the bi-Laplacian on a manifold with incomplete edge singularities. We employ a microlocal description of the biharmonic heat kernel to establish mapping…