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Two more counterexamples to the infinite dimensional carleson embedding theorem

Rydhe, Eskil LU (2018) In International Mathematics Research Notices 2018(24). p.7655-7680
Abstract

The existence of a counterexample to the infinite-dimensional Carleson embedding theorem has been established by Nazarov, Pisier, Treil, and Volberg. We provide an explicit construction of such an example. We also obtain a non-constructive example of particularly simple form; the density function of the measure (with respect to a certain weighted area measure) is the tensor-square of a Hilbert space-valued analytic function. This special structure of the measure has implications for Hankel-like operators appearing in control theory.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Mathematics Research Notices
volume
2018
issue
24
pages
26 pages
publisher
Oxford University Press
external identifiers
  • scopus:85062018052
ISSN
1073-7928
DOI
10.1093/imrn/rnx120
language
English
LU publication?
yes
id
06007637-64bd-4e7b-b003-accf0806cd46
date added to LUP
2019-03-08 12:29:47
date last changed
2021-08-18 05:12:19
@article{06007637-64bd-4e7b-b003-accf0806cd46,
  abstract     = {<p>The existence of a counterexample to the infinite-dimensional Carleson embedding theorem has been established by Nazarov, Pisier, Treil, and Volberg. We provide an explicit construction of such an example. We also obtain a non-constructive example of particularly simple form; the density function of the measure (with respect to a certain weighted area measure) is the tensor-square of a Hilbert space-valued analytic function. This special structure of the measure has implications for Hankel-like operators appearing in control theory.</p>},
  author       = {Rydhe, Eskil},
  issn         = {1073-7928},
  language     = {eng},
  number       = {24},
  pages        = {7655--7680},
  publisher    = {Oxford University Press},
  series       = {International Mathematics Research Notices},
  title        = {Two more counterexamples to the infinite dimensional carleson embedding theorem},
  url          = {http://dx.doi.org/10.1093/imrn/rnx120},
  doi          = {10.1093/imrn/rnx120},
  volume       = {2018},
  year         = {2018},
}