FREE OUTER FUNCTIONS IN COMPLETE PICK SPACES
(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:
https://lup.lub.lu.se/record/21151c86-5c70-41b2-8de0-ad6f90c812b1
- author
- Aleman, Alexandru LU ; Hartz, Michael ; McCarthy, John E. and Richter, Stefan
- organization
- publishing date
- 2023-03-01
- 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}}, }