相关论文: Heat Expansion and Zeta

Given a cone pseudodifferential operator $P$ we give a full asymptotic expansion as $t\to 0^+$ of the trace $\Tr Pe^{-tA}$, where $A$ is an elliptic cone differential operator for which the resolvent exists on a suitable region of the…

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…

Following the seminal works of Asorey-Ibort-Marmo and Mu\~{n}oz-Casta\~{n}eda-Asorey about selfadjoint extensions and quantum fields in bounded domains, we compute all the heat kernel coefficients for any strongly consistent selfadjoint…

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…

We get a generalization of Krein's formula -which relates the resolvents of different selfadjoint extensions of a differential operator with regular coefficients- to the non-regular case $A=-\partial_x^2+(\nu^2-1/4)/x^2+V(x)$, where…

The generator of time-translations on the solution space of the wave equation on stationary spacetimes specialises to the square root of the Laplacian on Riemannian manifolds when the spacetime is ultrastatic. Its spectral analysis…

We study heat traces associated with positive unbounded operators with compact inverses. With the help of the inverse Mellin transform we derive necessary conditions for the existence of a short time asymptotic expansion. The conditions are…

This paper is devoted to study the asymptotic expansion of the heat trace of the Dirichlet-to-Neumann map for the thermoelastic equation on a Riemannian manifold with doundary. By providing a method we can obtain all the coefficients of the…

We consider a quantum graph where the operator contains a potential. We show that this operator admits a heat kernel. Under some assumptions on the potential, this heat kernel admits an asymptotic expansion at t=0 with coefficients that…

The regularized trace of the heat kernel of a one-dimensional Schr\"odinger operator with a singular two-particle contact interaction being of Lieb-Liniger type is considered. We derive a complete small-time asymptotic expansion in…

The asymptotic expansion of the heat-kernel for small values of its argument has been studied in many different cases and has been applied to 1-loop calculations in Quantum Field Theory. In this thesis we consider this asymptotic behavior…

Denoting by $\Delta_\nu$ the Fubini-Study Laplacian perturbed by a uniform magnetic field strength proportional to $\nu$, this operator has a discrete spectrum consisting on eigenvalues $\beta_m, \ m\in\mathbb{Z}_+$, when acting on bounded…

We derive a detailed asymptotic expansion of the heat trace for the Laplace-Beltrami operator on functions on manifolds with conic singularities, using the Singular Asymptotics Lemma of Jochen Bruening and Robert T. Seeley [BS]. In the…

The square root of the heat operator $\sqrt{\partial_t-\Delta}$, can be realized as the Dirichlet to Neumann map of the heat extension of data on $\mathbb R^{n+1}$ to $\mathbb R^{n+2}_+$. In this note we obtain similar characterizations for…

In this paper we analyze the small-t asymptotic expansion of the trace of the heat kernel associated with a Laplace operator endowed with a spherically symmetric polynomially confining potential on the unbounded, d-dimensional Euclidean…

In this article we analyze the resolvent, the heat kernel and the spectral zeta function of the operator $-d^2/dr^2 - 1/(4r^2)$ over the finite interval. The structural properties of these spectral functions depend strongly on the chosen…

We present a systematic study of asymptotic behavior of (generalised) $\zeta-$functions and heat kernels used in noncommutative geometry and clarify their connections with Dixmier traces. We strengthen and complete a number of results from…

We give an asymptotic expansion of the relative entropy between the heat kernel $q_Z(t,z,w)$ of a compact Riemannian manifold $Z$ and the normalized Riemannian volume for small values of $t$ and for a fixed element $z\in Z$. We prove that…

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 study the relationship between the geometry and the Laplace spectrum of a Riemannian orbifold O via its heat kernel; as in the manifold case, the time-zero asymptotic expansion of the heat kernel furnishes geometric information about O.…