Related papers: The heat kernel and frequency localized functions …

We consider the heat equation $u_t=Lu$ where $L$ is a second-order difference operator in a discrete variable $n$. The fundamental solution has an expansion in terms of the Bessel functions of imaginary argument. The coefficients…

We prove sharp power-weighted $L^p$, weak type and restricted weak type inequalities for the heat semigroup maximal operator and Riesz transforms associated with the Bessel operator $B_{\nu}$ in the exotic range of the parameter $-\infty <…

We introduce a class of non-commutative, complex, infinite-dimensional Heisenberg like Lie groups based on an abstract Wiener space. The holomorphic functions which are also square integrable with respect to a heat kernel measure $\mu$ on…

This paper presents a detailed analysis of the heat kernel on an $(\mathbb{N}\times\mathbb{N})$-parameter family of compact metric measure spaces, which do not satisfy the volume doubling property. In particular, uniform bounds of the heat…

We study the geometry associated to the Grusin operator G=\Delta_{x}+|x|^{2}\partial_{u}^{2} on \mathbb{R}_{x}^{n}\times\mathbb{R}_{u}, to obtain heat kernel estimates for this operator. The main work is to find the shortest geodesics…

We study heat kernels of Schr\"odinger operators whose kinetic terms are non-local operators built for sufficiently regular symmetric L\'evy measures with radial decreasing profiles and potentials belong to Kato class. Our setting is fairly…

Nash and Sobolev inequalities are known to be equivalent to ultracontractive properties of heat-like Markov semigroups, hence to uniform on-diagonal bounds on their kernel densities. In non ultracontractive settings, such bounds can not…

We prove the following gradient inequality for the subelliptic heat kernel on nilpotent Lie groups $G$ of H-type: $$|\nabla P_t f| \le K P_t(|\nabla f|)$$ where $P_t$ is the heat semigroup corresponding to the sublaplacian on $G$, $\nabla$…

We develop connections between Harnack inequalities for the heat flow of diffusion operators with curvature bounded from below and optimal transportation. Through heat kernel inequalities, a new isoperimetric-type Harnack inequality is…

We suggest a method of reduction of mixed absolute and relative boundary conditions to pure ones. The case of rank two tensor is studied in detail. For four-dimensional disk the corresponding heat kernel is expressed in terms of scalar heat…

By adapting a technique of Molchanov, we obtain the heat kernel asymptotics at the sub-Riemannian cut locus, when the cut points are reached by an $r$-dimensional parametric family of optimal geodesics. We apply these results to the…

We study an index of a transversal Dirac operator on an odd-dimensional manifold $X$ with locally free $\mathbb{S}^1$-action. One difficulty of using heat kernel method lies in the understanding of the asymptotic expansion as $t\to 0^+$. By…

Following Osipov and Hiller, a generalized heat kernel expansion is considered for the effective action of bosonic operators. In this generalization, the standard heat kernel expansion, which counts inverse powers of a c-number mass…

A method for calculation of the DWSG coefficients for operators in spaces with metric incompatible with connection is suggested based on a generalization of the pseudodifferential operators technique. By using the proposed method, the…

We establish precise upper and lower bounds for the subelliptic heat kernel on nilpotent Lie groups $G$ of H-type. Specifically, we show that there exist positive constants $C_1$, $C_2$ and a polynomial correction function $Q_t$ on $G$ such…

Heat kernels arise in a variety of contexts including probability, geometry, and functional analysis; the automorphic heat kernel is particularly important in number theory and string theory. The typical construction of an automorphic heat…

We consider positive semidefinite kernels which have values given by bounded linear operators on certain bundles of Hilbert spaces and which are invariant under actions of $*$-semigroupoids. For these kernels, we prove that there exist…

We give the upper and the lower estimates of heat kernels for Schr\"odinger operators $H=-\Delta+V$, with nonnegative and locally bounded potentials $V$ in $\mathbb{R}^d$, $d \geq 1$. We observe a factorization: the contribution of the…

A non-relativistic quantum model is considered with a point particle carrying a charge $e$ and moving on the plane pierced by two infinitesimally thin Aharonov-Bohm solenoids and subjected to a perpendicular uniform magnetic field of…

We consider metric graphs with Kirchhoff boundary conditions. We study the intrinsic metric, volume doubling and a Poincar\'e inequality. This enables us to prove a parabolic Harnack inequality. The proof involves various techniques from…