Related papers: Heat trace asymptotics defined by transfer boundar…
The transfer operator associated to a flow (continuous time dynamical system) is a one-parameter operator semigroup. We consider the operator-valued Laplace transform of this one-parameter semigroup. Estimates on the Laplace transform have…
We obtain asymptotic expansions of the spatially discrete 2D heat kernels, or Green's functions on lattices, with respect to powers of time variable up to an arbitrary order and estimate the remainders uniformly on the whole lattice. Unlike…
We study the asymptotic behavior of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions imposing Robin boundary conditions. Assuming the existence of…
We study higher-order asymptotic expansions of eigenvalues in perturbed transfer operators, of the corresponding eigenfunctions and of the corresponding eigenvectors of the dual operators. In our main result, we give explicit expressions of…
It is known that in the zeta function regularization and in the Fujikawa method chiral anomaly is defined through a coefficient in the heat kernel expansion for the Dirac operator. In this paper we apply the heat kernel methods to calculate…
We calculate the heat-kernel coefficients, up to $a_2$, for a U(1) bundle on the 4-Ball for boundary conditions which are such that the normal derivative of the field at the boundary is related to a first-order operator in boundary…
We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential…
The asymptotics of a singularly perturbed problem is constructed. describing the transport of a polydisperse impurity in the atmosphere, taking into account the processes of precipitation and wind pick-up, as well as the processes of…
In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…
In this paper we extend our recent work on two-dimensional (2D) diffusive search-and-capture processes with multiple small targets (narrow capture problems) by considering an asymptotic expansion of the Laplace transformed probability flux…
This work consists in the asymptotic analysis of the solution of Poisson equation in a bounded domain of $\mathbb{R}^{P}$ $(P=2,3)$ with a thin layer. We use a method based on hierarchical variational equations to derive asymptotic…
Let -\Delta denote the Dirichlet Laplace operator on a bounded open set in \mathbb{R}^d. We study the sum of the negative eigenvalues of the operator -h^2 \Delta - 1 in the semiclassical limit h \to 0+. We give a new proof that yields not…
For incomplete sub-Riemannian manifolds, and for an associated second-order hypoelliptic operator, which need not be symmetric, we identify two alternative conditions for the validity of Gaussian-type upper bounds on heat kernels and…
Organic charge transfer salts exhibit thermal expansion anomalies similar to those found in other strongly correlated electron systems. The thermal expansion can be anisotropic and have a non-monotonic temperature dependence. We show how…
We study thermal processes in infinite harmonic crystals having a unit cell with arbitrary number of particles. Initially particles have zero displacements and random velocities, corresponding to some initial temperature profile. Our main…
We consider Laplace operators on metric graphs, networks of one-dimensional line segments (bonds), with matching conditions at the vertices that make the operator self-adjoint. Such quantum graphs provide a simple model of quantum mechanics…
This paper presents a novel way of computing front positions in Fisher-KPP equations. Our method is based on an exact relation between the Laplace transform of the initial condition and some integral functional of the front position. Using…
We present a new functional setting for Neumann conditions related to the superposition of (possibly infinitely many) fractional Laplace operators. We will introduce some bespoke functional framework and present minimization properties,…
In this work a discontinuous boundary-value problem with retarded argument which contains spectral parameter in the transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues…
A broad class of inverse problems deals with determining certain parameters, from measurement data, in models which are associated to certain partial differential equations. In this work we focus on the heat equation on a finite interval…