The Laplace Operator in an Orthant (Algebraic Geometry Approach)

#### A.I. Ovseevich

1995, v.1, №1, 79-90

ABSTRACT

Explicit integral formulas for the resolvent of the discrete Laplace operator in an orthant are obtained, thus providing an analytic continuation of the resolvent. A homological approach to the problem of the inversion of Toeplitz operators is developed.

Keywords: Toeplitz operators,Cech cohomology,Bergman-Weil integral representation,random walks in an orthant