Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9503153 | Journal of Mathematical Analysis and Applications | 2005 | 14 Pages |
Abstract
We find the singular values and corresponding Schmidt pairs of a compact composition operator CÏ induced by Ï(z)=az+b, where |a|+|b|<1, on the classical Hardy space. We do so by solving a functional equation that is a generalization of Schröder's equation: find a function f, holomorphic on the open unit disc, and a complex number λ such that G(z)f(Ï(z))=λf(Ï(z)), where Ï is a holomorphic self-map of the open unit disc with an interior fixed point and G is a bounded holomorphic function on the open unit disc. In addition, we find the spectrum of the weighted composition operator MGCÏ.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
John H. Clifford, Michael G. Dabkowski,