Related papers: Non-divergence operators structured on homogeneous…
Using the result by D.Gessler (Differential Geom. Appl. 7 (1997) 303-324, DIPS-9/98, http://diffiety.ac.ru/preprint/98/09_98abs.htm), we show that any invariant variational bivector (resp., variational 2-form) on an evolution equation with…
The principal aim of this short note is to extend a recent result on Gaussian heat kernel bounds for self-adjoint $L^2(\Om; d^n x)$-realizations, $n\in\bbN$, $n\geq 2$, of divergence form elliptic partial differential expressions $L$ with…
We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This rises certain…
The classical divergence theorem for an $n$-dimensional domain $A$ and a smooth vector field $F$ in $n$-space $$\int_{\partial A} F \cdot n = \int_A div F$$ requires that a normal vector field $n(p)$ be defined a.e. $p \in \partial A$. In…
A persistence diagram is a finite multiset of birth-death pairs representing the lifetimes of topological features across a filtration. Persistence diagrams do not carry intrinsic spectral or kernel structures, so applications typically use…
Given a real reductive group $G$, the purpose of this paper is to show an asymptotic formula of the large-time behavior of the $G$-trace of the heat operator on the associated symmetric spaces. Together with Carmona's proof on Vogan's…
Consider $\beta > 1$ and $\lfloor \beta \rfloor$ its integer part. It is widely known that any real number $\alpha \in \Bigl[0, \frac{\lfloor \beta \rfloor}{\beta - 1}\Bigr]$ can be represented in base $\beta$ using a development in series…
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…
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.…
The paper deals with homogenization problem for a non-local linear operator with a kernel of convolution type in a medium with a periodic structure. We consider the natural diffusive scaling of this operator and study the limit behaviour of…
We prove heat kernel estimates for the $\bar\partial$-Neumann Laplacian acting in spaces of differential forms over noncompact, strongly pseudoconvex complex manifolds with a Lie group symmetry and compact quotient. We also relate our…
Let $L = -1/4 (\sum_{j=1}^n(X_j^2+Y_j^2)+i\gamma T)$ where $\gamma$ is a complex number, $X_j$, $Y_j$, and $T$ are the left invariant vector fields of the Heisenberg group structure for $R^n \times R^n \times R$. We explicitly compute the…
An overview about recent progress in the calculation of the heat kernel and the one-loop effective action in quantum gravity and gauge theories is given. We analyse the general structure of the standard Schwinger-De Witt asymptotic…
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The associated diffusion operator is…
The spectrum of the fermionic operators depending on external fields is an important object in Quantum Field Theory. In this paper we prove, using transition to the alternative basis for the $\gamma$-matrices, that this spectrum does not…
We study homogeneous Besov and Triebel--Lizorkin spaces defined on doubling metric measure spaces in terms of a self-adjoint operator whose heat kernel satisfies Gaussian estimates together with its derivatives. When the measure space is a…
We develop a phase-space framework for fractional generalised anharmonic oscillators and their heat semigroups on weighted modulation spaces. We consider operators of the form \[ \mathcal{H}_{k,l}=(-\Delta)^{l}+V(x), \] where $V$ is a…
From \cite{re} From \cite{re} it is known that ``translation-invariant Gibbs measures" of the model with an uncountable set of spin values can be described by positive fixed points of a nonlinear integral operator of Hammerstein type. In…
We review the status of covariant methods in quantum field theory and quantum gravity, in particular, some recent progress in the calculation of the effective action via the heat kernel method. We study the heat kernel associated with an…
We survey the recent progress in the study of heat kernels for a class of non-symmetric non-local operators. We focus on the existence and sharp two-sided estimates of the heat kernels and their connection to jump diffusions.