Conjugation, the Backward Shift, and Toeplitz Kernels
Document Type
Article
Department
Mathematics (Pomona)
Publication Date
2005
Keywords
conjugation, backward shift, Toeplitz kernels, pseudocontinuations, Darlington synthesis problem, electrical network theory
Abstract
For each outer function $\Omega$ in the Smirnov class and each $p \in (0,\infty)$, we define a subspace $\mathcal{N}_{\Omega}^p$ of $H^p$ that carries an operation analogous to complex conjugation. Using these subspaces, we explicitly describe the invariant subspaces and noncyclic functions for the backward shift operator on $H^p$ for $p \in [1,\infty)$ and $p \in (0,\infty)$, respectively. We also discuss pseudocontinuations, the Darlington synthesis problem from electrical network theory, and the kernels of Toeplitz operators.
Rights Information
© 2005 Theta Foundation
Terms of Use & License Information
Recommended Citation
Garcia, S.R., Conjugation, the backward shift, and Toeplitz kernels, J. Operator Theory 54, no. 2, (2005), 239–250. MR2186351 (2006g:30055)
