Nehari's Theorem for Convex Domain Hankel and Toeplitz Operators in Several Variables
(2021) In International Mathematics Research Notices 2021(5). p.33313361 Abstract
We prove Nehari s theorem for integral Hankel and Toeplitz operators on simple convex polytopes in several variables. A special case of the theorem, generalizing the boundedness criterion of the Hankel and Toeplitz operators on the Paley Wiener space, reads as follows. Let = (0, 1)d be a ddimensional cube, and for a distribution f on 2, consider the Hankel operator f (g)(x) = λ f (x + y)g(y) dy, x Then λf extends to a bounded operator on L2 if and only if there is a bounded function b on Rd whose Fourier transform coincides with f on 2. This special case has an immediate application in matrix extension theory: every finite multilevel block Toeplitz matrix can be boundedly extended to an infinite multilevel block Toeplitz matrix. In... (More)
We prove Nehari s theorem for integral Hankel and Toeplitz operators on simple convex polytopes in several variables. A special case of the theorem, generalizing the boundedness criterion of the Hankel and Toeplitz operators on the Paley Wiener space, reads as follows. Let = (0, 1)d be a ddimensional cube, and for a distribution f on 2, consider the Hankel operator f (g)(x) = λ f (x + y)g(y) dy, x Then λf extends to a bounded operator on L2 if and only if there is a bounded function b on Rd whose Fourier transform coincides with f on 2. This special case has an immediate application in matrix extension theory: every finite multilevel block Toeplitz matrix can be boundedly extended to an infinite multilevel block Toeplitz matrix. In particular, block Toeplitz operators with blocks that are themselves Toeplitz can be extended to bounded infinite block Toeplitz operators with Toeplitz blocks.
(Less)
 author
 Carlsson, Marcus ^{LU} and Perfekt, Karl Mikael ^{LU}
 organization
 publishing date
 202103
 type
 Contribution to journal
 publication status
 published
 subject
 in
 International Mathematics Research Notices
 volume
 2021
 issue
 5
 pages
 31 pages
 publisher
 Oxford University Press
 external identifiers

 scopus:85126309075
 ISSN
 10737928
 DOI
 10.1093/imrn/rnz193
 language
 English
 LU publication?
 yes
 id
 9fce41c0dc5249458306065062cc543e
 date added to LUP
 20220502 15:21:23
 date last changed
 20230510 14:07:05
@article{9fce41c0dc5249458306065062cc543e, abstract = {{<p>We prove Nehari s theorem for integral Hankel and Toeplitz operators on simple convex polytopes in several variables. A special case of the theorem, generalizing the boundedness criterion of the Hankel and Toeplitz operators on the Paley Wiener space, reads as follows. Let = (0, 1)d be a ddimensional cube, and for a distribution f on 2, consider the Hankel operator f (g)(x) = λ f (x + y)g(y) dy, x Then λf extends to a bounded operator on L2 if and only if there is a bounded function b on Rd whose Fourier transform coincides with f on 2. This special case has an immediate application in matrix extension theory: every finite multilevel block Toeplitz matrix can be boundedly extended to an infinite multilevel block Toeplitz matrix. In particular, block Toeplitz operators with blocks that are themselves Toeplitz can be extended to bounded infinite block Toeplitz operators with Toeplitz blocks.</p>}}, author = {{Carlsson, Marcus and Perfekt, Karl Mikael}}, issn = {{10737928}}, language = {{eng}}, number = {{5}}, pages = {{33313361}}, publisher = {{Oxford University Press}}, series = {{International Mathematics Research Notices}}, title = {{Nehari's Theorem for Convex Domain Hankel and Toeplitz Operators in Several Variables}}, url = {{http://dx.doi.org/10.1093/imrn/rnz193}}, doi = {{10.1093/imrn/rnz193}}, volume = {{2021}}, year = {{2021}}, }