相关论文: Heat Trace Asymptotics on Noncommutative Spaces

We study the heat trace for both the drifting Laplacian as well as Schr\"odinger operators on compact Riemannian manifolds. In the case of a finite regularity potential or weight function, we prove the existence of a partial (six term)…

We discuss the exotic properties of the heat-trace asymptotics for a regular-singular operator with general boundary conditions at the singular end, as observed by Falomir, Muschietti, Pisani and Seeley as well as by Kirsten, Loya and Park.…

The formulation of gauge theories on compact Riemannian manifolds with boundary leads to partial differential operators with Gilkey--Smith boundary conditions, whose peculiar property is the occurrence of both normal and tangential…

We explicitly evaluate the heat kernel for the Laplacian of arbitrary spin tensor fields on the thermal quotient of (Euclidean) $AdS_N$ for $N\geq 3$ using the group theoretic techniques employed for $AdS_3$ in arXiv:0911.5085. Our approach…

We prove that the heat equation on $\mathbb{R}^d$ is well-posed in certain spaces of functions allowing spatial asymptotic expansions as $|x|\to\infty$ of any a priori given order. In fact, we show that the Laplacian on such function spaces…

By applying the covariant Taylor expansion method, the fifth lower coefficients the asymptotic expansion of the heat kernel associated with a fermion of spin 1/2 in Riemann-Cartan space are manifestly given. These coefficients in…

The principal object in noncommutatve geometry is the spectral triple consisting of an algebra A, a Hilbert space H, and a Dirac operator D. Field theories are incorporated in this approach by the spectral action principle, that sets the…

In this paper, we investigate the long-time structure of the heat kernel on a Riemannian manifold M which is asymptotically conic near infinity. Using geometric microlocal analysis and building on results of Guillarmou and Hassell on the…

Given i.i.d. observations uniformly distributed on a closed manifold $\mathcal{M}\subseteq \mathbb{R}^p$, we study the spectral properties of the associated empirical graph Laplacian based on a Gaussian kernel. Our main results are…

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…

The spectral heat content is investigated for time-changed killed Brownian motions on C1,1 open sets, where the time change is given by either a subordinator or an inverse subordinator, with the underlying Laplace exponent being regularly…

The spectral problem where the field satisfies Dirichlet conditions on one part of the boundary of the relevant domain and Neumann on the remainder is discussed. It is shown that there does not exist a classical asymptotic expansion for…

We calculate the closed analytic form of the solution of heat kernel equation for the anisotropic generalizations of flat Laplacian. We consider a UV as well as UV/IR interpolating generalizations. In all cases, the result can be expressed…

We analyze the spectra of general non-minimal second-order operators. To do this, we derive the local part of the trace of the second Seeley-DeWitt heat kernel coefficient for such operators in a completely model-independent way.…

We consider sub-Laplacians in open bounded sets in a homogeneous Carnot group and study their spectral properties. We prove that these operators have a pure point spectrum, and prove the existence of the spectral gap. In addition, we give…

We establish the large-$N$ asymptotic expansion of the (central) trace of the heat kernel on any compact classical group $G_N\subset\mathrm{GL}_N(\mathbb{C})$, which extends a previous result known only for $\mathrm{U}(N)$ \cite{LM2}. It…

We present an ab initio approach to integration theory for nonunital spectral triples. This is done without reference to local units and in the full generality of semifinite noncommutative geometry. The main result is an equality between…

The operator $e^{-tA}$ and its trace are investigated in the case when $A$ is a non-self-adjoint elliptic differential operator on a manifold with conical singularities. Under a certain spectral condition (parameter-ellipticity) we obtain a…

Let $\mathcal{M}$ be a smooth, closed and connected manifold of dimension $n\in\mathbb{N}$, endowed with a Riemannian metric $g$. Moreover, let $\mathcal{B}$ be an $(n+1)$-dimensional compact manifold with boundary equal to $\mathcal{M}$.…

Heat kernel expansion coefficients are calculated for vacuum fluctuations with distributional background potentials and field strengths. Terms up to and including t^5/2 are presented.