Note on Gradient Estimate of Heat Kernel for Schrödinger Operators

A note on the heat kernel coefficients for nonminimal operators

We consider certain results for the heat kernel of nonminimal operators. The general expressions provided by Gusynin and Kornyak resulting from symbolic computation programmes for n dimensions are evaluated for 4 dimensions which are checked against results given by Barvinsky and Vilkovisky. We also check that the results in flat space are consistent with earlier results of Guendelmen et al. We...

A Note on Heat Kernel Estimates for Second-order Elliptic Operators

We study fundamental solutions to second order parabolic systems of divergence type with time independent coefficients, and give another proof of a result by Auscher, McIntosh and Tchamitchian on the Gaussian bounds for the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients.

An Estimate on the Heat Kernel of Magnetic Schrödinger Operators and Unformly Elliptic Operators with Non–negative Potentials

Full bandwidth matrix selectors for gradient kernel density estimate

The most important factor in multivariate kernel density estimation is a choice of a bandwidth matrix. This choice is particularly important, because of its role in controlling both the amount and the direction of multivariate smoothing. Considerable attention has been paid to constrained parameterization of the bandwidth matrix such as a diagonal matrix or a pre-transformation of the data. A g...

An Estimate on the Heat Kernel ofMagnetic Schr