The Invariance of the Index of Elliptic Operators, elliptic operators

Chia sẻ: Lê Duy Vinh | Ngày: | Loại File: PDF | Số trang:41

0
90
lượt xem
10
download

The Invariance of the Index of Elliptic Operators, elliptic operators

Mô tả tài liệu
  Download Vui lòng tải xuống để xem tài liệu đầy đủ

Abstract In 1963 Atiyah and Singer proved the famous Atiyah-Singer Index Theorem, which states, among other things, that the space of elliptic pseudodifferential operators is such that the collection of operators with any given index forms a connected subset. Contained in this statement is the somewhat more specialized claim that the index of an elliptic operator must be invariant under sufficiently small perturbations. By developing the machinery of distributions and in particular Sobolev spaces, this paper addresses this more specific part of the famous Theorem from a completely analytic approach. We first prove the regularity of elliptic operators, then the...

Chủ đề:
Lưu

Nội dung Text: The Invariance of the Index of Elliptic Operators, elliptic operators

Đồng bộ tài khoản