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AN ESTIMATE ON THE HEAT KERNEL OF MAGNETIC SCHRÖDINGER OPERATORS AND UNIFORMLY ELLIPTIC OPERATORS WITH NON-NEGATIVE POTENTIALS

Published online by Cambridge University Press:  13 February 2001

KAZUHIRO KURATA
KAZUHIRO KURATA
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo, Japan; kurata@comp.metro-u.ac.jp
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Abstract

The paper studies the heat kernel of the Schrödinger operator with magnetic fields and of uniformly elliptic operators with non-negative electric potentials in the reverse Hölder class which includes non-negative polynomials as typical examples. The main aim of the paper is to give a pointwise estimate of the heat kernel of the operators above which is affected by magnetic fields and non-negative degenerate electric potentials. A weighted smoothing estimate for the semigroup generated by the operators above is also given.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 62 , Issue 3 , December 2000 , pp. 885 - 903
Copyright
The London Mathematical Society 2000

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