Related papers: On an approach for evaluating certain trigonometri…
A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as…
In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational…
We consider a natural generalisation of the Laplace type operators for the case of non-commutative (Moyal star) product. We demonstrate existence of a power law asymptotic expansion for the heat kernel of such operators on T^n. First four…
In this thesis a connection between the worlds of discrete and continuous conformal geometry is explored. Specifically, a disk pattern production theroem is proved using an energy which measures how ``uniform'' the angle data of a…
Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients and a possibly unbounded potential term.
For the discrete Laguerre operators we compute explicitly the corresponding heat kernels by expressing them with the help of Jacobi polynomials. This enables us to show that the heat semigroup is ultracontractive and to compute the…
We display an interesting sum rule for the dynamical thermal conductivity for many standard models of condensed matter in terms of the expectation of a thermal operator. We present the thermal operator for several model systems of current…
The contributions to the heat kernel coefficients generated by the corners of the boundary are studied. For this purpose the internal and external sectors of a wedge and a cone are considered. These sectors are obtained by introducing,…
Let $Z=(Z^{1}, \ldots, Z^{d})$ be the d-dimensional L\'evy {process} where {$Z^i$'s} are independent 1-dimensional L\'evy {processes} with identical jumping kernel $ \nu^1(r) =r^{-1}\phi(r)^{-1}$. Here $\phi$ is {an} increasing function…
We study the heat kernel for an operator of Laplace type with a $\delta$-function potential concentrated on a closed surface. We derive the general form of the small $t$ asymptotics and calculate explicitly several first heat kernel…
The generalized summation of divergent trigonometric series, namely by method of $\sigma_k(r,a)$-factors is considered in this paper. It is proved that such summation of Fourier series of periodical function $f(t)$ results in the…
Our goal in this paper is to solve the 1-D heat equation by an hybrid deterministic-stochastic iterative procedure . The deterministic side consists in discretizing the equation by the Crank-Nicolson method and the stochastic side consists…
In this paper, we investigate the determinants involving some trigonometric functions. We establish a connection between these determinants and the special values of Dirichlet L-functions, thereby extending Guo's results to arbitrary…
We obtain matching two sided estimates of the heat kernel on a connected sum of parabolic manifolds, each of them satisfying the Li-Yau estimate. The key result is the on-diagonal upper bound of the heat kernel at a central point. Contrary…
The phenomenon of hysteresis is commonly observed in many UV thermal experiments involving unmodified or modified nucleic acids. In presence of hysteresis, the thermal curves are irreversible and demand a significant effort to produce the…
In this article, we consider flat and curved Riemannian symmetric spaces in the complex case and we study their basic integral kernels, in potential and spherical analysis: heat, Newton, Poisson kernels and spherical functions, i.e. the…
Let $d\ge1$ and $0<\alpha<2$. Consider the integro-differential operator \[ \mathcal{L}f(x) =\int_{\mathbb{R}^{d}\backslash\{0\}}\left[f(x+h)-f(x)-\chi_{\alpha}(h)\nabla f(x)\cdot…
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 develop a diagrammatic approach for calculating the high temperature expansion of dynamic correlation functions, such as the electron Green's function and the time-dependent density-density and spin-spin correlation functions, for the…
We obtain two-sided estimates for the heat kernel (or the fundamental function) associated with the following fractional Schr\"odinger operator with negative Hardy potential $$\Delta^{\alpha/2} -\lambda |x|^{-\alpha}$$ on $\RR^d$, where…