Monotone operator functions, gaps and power moment problem
(2007) In Mathematica Scandinavica 100(1). p.161183 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 Pn(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 Pn(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:
http://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
 00255521
 language
 English
 LU publication?
 yes
 id
 7f371a748e52464abe6e8ec778f9b534 (old id 647671)
 alternative location
 http://www.mscand.dk/article.php?id=3009
 date added to LUP
 20071217 08:50:17
 date last changed
 20180107 09:50:09
@article{7f371a748e52464abe6e8ec778f9b534, 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 Pn(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 = {00255521}, language = {eng}, number = {1}, pages = {161183}, publisher = {Matematisk Institut}, series = {Mathematica Scandinavica}, title = {Monotone operator functions, gaps and power moment problem}, volume = {100}, year = {2007}, }