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FREE OUTER FUNCTIONS IN COMPLETE PICK SPACES

Aleman, Alexandru LU ; Hartz, Michael ; McCarthy, John E. and Richter, Stefan (2023) In Transactions of the American Mathematical Society 376(3). p.1929-1978
Abstract

Jury and Martin establish an analogue of the classical inner-outer factorization of Hardy space functions. They show that every function f in a Hilbert function space with a normalized complete Pick reproducing kernel has a factorization of the type f = ϕg, where g is cyclic, ϕ is a contractive multiplier, and ||f|| = ||g||. In this paper we show that if the cyclic factor is assumed to be what we call free outer, then the factors are essentially unique, and we give a characterization of the factors that is intrinsic to the space. That lets us compute examples. We also provide several applications of this factorization.

Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Transactions of the American Mathematical Society
volume
376
issue
3
pages
50 pages
publisher
American Mathematical Society (AMS)
external identifiers
  • scopus:85149204088
ISSN
0002-9947
DOI
10.1090/tran/8812
language
English
LU publication?
yes
id
21151c86-5c70-41b2-8de0-ad6f90c812b1
date added to LUP
2023-03-14 11:04:59
date last changed
2023-03-14 11:04:59
@article{21151c86-5c70-41b2-8de0-ad6f90c812b1,
  abstract     = {{<p>Jury and Martin establish an analogue of the classical inner-outer factorization of Hardy space functions. They show that every function f in a Hilbert function space with a normalized complete Pick reproducing kernel has a factorization of the type f = ϕg, where g is cyclic, ϕ is a contractive multiplier, and ||f|| = ||g||. In this paper we show that if the cyclic factor is assumed to be what we call free outer, then the factors are essentially unique, and we give a characterization of the factors that is intrinsic to the space. That lets us compute examples. We also provide several applications of this factorization.</p>}},
  author       = {{Aleman, Alexandru and Hartz, Michael and McCarthy, John E. and Richter, Stefan}},
  issn         = {{0002-9947}},
  language     = {{eng}},
  month        = {{03}},
  number       = {{3}},
  pages        = {{1929--1978}},
  publisher    = {{American Mathematical Society (AMS)}},
  series       = {{Transactions of the American Mathematical Society}},
  title        = {{FREE OUTER FUNCTIONS IN COMPLETE PICK SPACES}},
  url          = {{http://dx.doi.org/10.1090/tran/8812}},
  doi          = {{10.1090/tran/8812}},
  volume       = {{376}},
  year         = {{2023}},
}