Year: 2000
Type: preprint
Abstract: . For several classes of pseudodifferential operators with operator-valued symbol analytic index formulas are found. The common feature is that usual index formulas are not valid for these operators. Applications are given to pseudodifferential operators on singular manifolds. 1. Introduction Analytical index formulas play an important part in the study of topological characteristics of elliptic operators. They complement index formulas expressed in topological and algebraical terms, and often enter in these formulas as an ingredient. For elliptic pseudodifferential operators on compact manifolds, such formulas were found by Fedosov [F1]; later, analytical index formulas for elliptic boundary value problems were obtained in [F2]. These formulas have a common feature: they involve an integral, with integrand containing analytical expressions for the classical characteristic classes entering into the co-homological formulas. In 90-s a systematic study started of topological charact...
Author: Grigori Rozenblum
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3110027329