Related papers: A heat kernel proof of the index theorem for defor…
In this preprint the notion of deformation quantization of endomorphism bundles over symplectic manifolds is defined and developed, including index theory.
We establish heat kernel and gradient estimates for the density of kinetic degenerate Kolmogorov stochastic differentia equations. Our results are established under somehow minimal assumptions that guarantee the SDE is weakly well posed.
This paper is an overview on our recent results in the calculation of the heat kernel in quantum field theory and quantum gravity. We introduce a deformation of the background fields (including the metric of a curved spacetime manifold) and…
We present a new smooth, Gaussian-like kernel that allows the kernel density estimate for an angular distribution to be exactly represented by a finite number of its Fourier series coefficients. Distributions of angular quantities, such as…
The heat kernel associated with an elliptic second-order partial differential operator of Laplace type acting on smooth sections of a vector bundle over a Riemannian manifold, is studied. A general manifestly covariant method for…
We suggest a systematic calculational scheme for heat kernels of covariant nonminimal operators in causal theories whose characteristic surfaces are null with respect to a generic metric. The calculational formalism is based on a…
Let M be a compact complex surface which admits a Kaehler metric whose scalar curvature has integral zero; and suppose the fundamental group of M does not contain an Abelian subgroup of finite index. Then if M is blown up at sufficiently…
We discover a new, non-radial example of a manifold whose heat kernel decreases monotonically along all minimal geodesics. We also classify the flat tori with this monotonicity property. Furthermore, we show that for a generic metric on any…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
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 paper, we study quantization on a compact integral symplectic manifold $X$ with transversal real polarizations. In the case of complex polarizations, namely $X$ is K\"ahler equipped with transversal complex polarizations $T^{1, 0}X,…
On a compact Kahler manifold, one can define global invariants by integrating local invariants of the metric. Assume that a global invariant thus obtained depends only on the Kahler class. Then we show that the integrand can be decomposed…
In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star…
In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres.…
In this note we show the optimal gradient estimate for heat kernels of stable-like operators by providing a counterexample.
We study generalized heat kernel coefficients, which appear in the trace of the heat kernel with an insertion of a first-order differential operator, by using a path integral representation. These coefficients may be used to study…
The formulation of gauge theories on compact Riemannian manifolds with boundary leads to partial differential operators with Gilkey--Smith boundary conditions, whose peculiar property is the occurrence of both normal and tangential…
We investigate the heat kernel with Robin boundary condition and prove comparison theorems for heat kernel on geodesic balls and on minimal submanifolds. We also prove an eigenvalue comparison theorem for the first Robin eigenvalues on…
A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. The Hilbert space of states is realized via the Bott-Borel-Weil theorem in…
We study the spectrum and heat kernel of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold degenerating to a manifold with wedge singularities. Provided the Hodge Laplacians in the fibers of the wedge have an…