Monotone operator functions, gaps and power moment problem
(2007) In Mathematica Scandinavica 100(1). p.161-183- Abstract
- The article is devoted to investigation of the classes of functions belonging to the gaps between classes Pn+1 (I) and P, (I) of matrix monotone functions for full matrix algebras of successive dimensions. In this paper we address the problem of characterizing polynomials belonging to the gaps P-n(I) Pn+1 (I) for bounded intervals L We show that solution of this problem is closely linked to solution of truncated moment problems, Hankel matrices and Hankel extensions. Namely, we show that using the solutions to truncated moment problems we can construct continuum many polynomials in the gaps. We also provide via several examples some first insights into the further problem of description of polynomials in the gaps that are not coming from... (More)
- The article is devoted to investigation of the classes of functions belonging to the gaps between classes Pn+1 (I) and P, (I) of matrix monotone functions for full matrix algebras of successive dimensions. In this paper we address the problem of characterizing polynomials belonging to the gaps P-n(I) Pn+1 (I) for bounded intervals L We show that solution of this problem is closely linked to solution of truncated moment problems, Hankel matrices and Hankel extensions. Namely, we show that using the solutions to truncated moment problems we can construct continuum many polynomials in the gaps. We also provide via several examples some first insights into the further problem of description of polynomials in the gaps that are not coming from the truncated moment problem. Also, in this article, we deepen further in another way into the structure of the classes of matrix monotone functions and of the gaps between them by considering the problem of position in the gaps of certain interesting subclasses of matrix monotone functions that appeared in connection to interpolation of spaces and in a proof of the Lowner theorem on integral representation of operator monotone functions. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/647671
- author
- Osaka, Hiroyuki ; Silvestrov, Sergei LU and Tomiyama, Jun
- organization
- publishing date
- 2007
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Mathematica Scandinavica
- volume
- 100
- issue
- 1
- pages
- 161 - 183
- publisher
- Matematisk Institut
- external identifiers
-
- wos:000247570100006
- scopus:34248548897
- ISSN
- 0025-5521
- language
- English
- LU publication?
- yes
- id
- 7f371a74-8e52-464a-be6e-8ec778f9b534 (old id 647671)
- alternative location
- http://www.mscand.dk/article.php?id=3009
- date added to LUP
- 2016-04-01 17:13:19
- date last changed
- 2022-01-29 01:11:47
@article{7f371a74-8e52-464a-be6e-8ec778f9b534,
abstract = {{The article is devoted to investigation of the classes of functions belonging to the gaps between classes Pn+1 (I) and P, (I) of matrix monotone functions for full matrix algebras of successive dimensions. In this paper we address the problem of characterizing polynomials belonging to the gaps P-n(I) Pn+1 (I) for bounded intervals L We show that solution of this problem is closely linked to solution of truncated moment problems, Hankel matrices and Hankel extensions. Namely, we show that using the solutions to truncated moment problems we can construct continuum many polynomials in the gaps. We also provide via several examples some first insights into the further problem of description of polynomials in the gaps that are not coming from the truncated moment problem. Also, in this article, we deepen further in another way into the structure of the classes of matrix monotone functions and of the gaps between them by considering the problem of position in the gaps of certain interesting subclasses of matrix monotone functions that appeared in connection to interpolation of spaces and in a proof of the Lowner theorem on integral representation of operator monotone functions.}},
author = {{Osaka, Hiroyuki and Silvestrov, Sergei and Tomiyama, Jun}},
issn = {{0025-5521}},
language = {{eng}},
number = {{1}},
pages = {{161--183}},
publisher = {{Matematisk Institut}},
series = {{Mathematica Scandinavica}},
title = {{Monotone operator functions, gaps and power moment problem}},
url = {{http://www.mscand.dk/article.php?id=3009}},
volume = {{100}},
year = {{2007}},
}