HUSCAP logo Hokkaido Univ. logo

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

Files in This Item:
pre542.pdf236.98 kBPDFView/Open
Please use this identifier to cite or link to this item:http://doi.org/10.14943/83687

Title: The Nevanlinna counting functions for Rudin's orthogonal functions
Authors: Nakazi, T. Browse this author
Issue Date: Dec-2001
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

Export metadata:

OAI-PMH ( junii2 , jpcoar )


 

Feedback - Hokkaido University