Function-theoretic Operator Theory on Finitely Connected Planar Domains
Author | : Vinh-Thy Minh Tran |
Publisher | : |
Total Pages | : |
Release | : 1998 |
ISBN-10 | : OCLC:72071085 |
ISBN-13 | : |
Rating | : 4/5 (85 Downloads) |
Download or read book Function-theoretic Operator Theory on Finitely Connected Planar Domains written by Vinh-Thy Minh Tran and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We generalize to finitely connected planar domains some classical results concerning composition operators and Toeplitz operators on the Hardy space and Bergman space of the unit disc. In particular, we study how operator-theoretic issues such as compactness and membership in Schattan classes are connected to function-theoretic issues such a value distribution, angular derivatives, and average growth near the boundary. In the process, we also obtain some boundary estimates involving the decay of the Green's function and the growth of certain reproducing kernels.