|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
The Nevanlinna counting functions for Rudin's orthogonal functions
| Title: | The Nevanlinna counting functions for Rudin's orthogonal functions |
| Authors: | Nakazi, T. Browse this author |
| Issue Date: | Dec-2001 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 542 |
| Start Page: | 1 |
| End Page: | 7 |
| Abstract: | H∞ and H2 denote the Hardy spaces on the open unit disc: D. Let cf> be a function in H∞ and 11</Jll ∞ = 1. If cf> is an inner function and ¢(0) = 0, then { cpn ; n = 0, 1, 2, · · ·} is orthogonal in H2 . \\7.Rudin asked if the converse is true and C.Sundberg and C.Bishop showed that the converse is not true. Therefore there exists a function c/J such that c/J is not an inner function and { c/Jn } is orthogonal in H2. In this paper, the following is shown : { q'Jn } is orthogonal in H2 if and only if there exists a uniqueprobability measure v0 on [0,1] with 1 E supp v0 such that N4,(z) - S log r/|z| dv0(r) for nearly all z in D where Nc/J is the Nevanlinna counting function of c/J. If 6 is an inner function, then v0 is a Dirac: measure at r = 1. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69291 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
|
Submitter: 数学紀要登録作業用
|
