An index formula for 𝑛-tuple of shifts on polydisk

Yan, Ke Ren

doi:10.1090/S0002-9939-1994-1185275-3

An index formula for $n$-tuple of shifts on polydisk
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Proc. Amer. Math. Soc. 121 (1994), 747-754 Request permission

Abstract:

Let $({M_{{z_1}}}, \ldots ,{M_{{z_n}}})$ be an n-tuple of shift operators on the polydisk ${l^2}({{\mathbf {Z}}^n})$; we compress it to a variety of subspaces of ${l^2}({{\mathbf {Z}}^n})$ that are combinatorially constructed. The main result is a multivariate Fredholm index formula, which links the indices of the n-tuples to their combinatorial data in the definitions of the subspaces.

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Hermitian sheaves and operator theory