Failure of Nehari's theorem for multiplicative Hankel forms in Schatten classes

Ole Fredrik Brevig, and Karl-Mikael Perfekt. "Failure of Nehari's theorem for multiplicative Hankel forms in Schatten classes." Studia Mathematica 228.2 (2015): 101-108. <http://eudml.org/doc/285417>.

@article{OleFredrikBrevig2015,
abstract = {Ortega-Cerdà-Seip demonstrated that there are bounded multiplicative Hankel forms which do not arise from bounded symbols. On the other hand, when such a form is in the Hilbert-Schmidt class ₂, Helson showed that it has a bounded symbol. The present work investigates forms belonging to the Schatten classes between these two cases. It is shown that for every $p > (1- log π/log 4)^\{-1\}$ there exist multiplicative Hankel forms in the Schatten class $_\{p\}$ which lack bounded symbols. The lower bound on p is in a certain sense optimal when the symbol of the multiplicative Hankel form is a product of homogeneous linear polynomials.},
author = {Ole Fredrik Brevig, Karl-Mikael Perfekt},
journal = {Studia Mathematica},
keywords = {Hankel forms; infinite-dimensional torus; Schatten class; Nehari's theorem; Dirichlet series},
language = {eng},
number = {2},
pages = {101-108},
title = {Failure of Nehari's theorem for multiplicative Hankel forms in Schatten classes},
url = {http://eudml.org/doc/285417},
volume = {228},
year = {2015},
}

TY - JOUR
AU - Ole Fredrik Brevig
AU - Karl-Mikael Perfekt
TI - Failure of Nehari's theorem for multiplicative Hankel forms in Schatten classes
JO - Studia Mathematica
PY - 2015
VL - 228
IS - 2
SP - 101
EP - 108
AB - Ortega-Cerdà-Seip demonstrated that there are bounded multiplicative Hankel forms which do not arise from bounded symbols. On the other hand, when such a form is in the Hilbert-Schmidt class ₂, Helson showed that it has a bounded symbol. The present work investigates forms belonging to the Schatten classes between these two cases. It is shown that for every $p > (1- log π/log 4)^{-1}$ there exist multiplicative Hankel forms in the Schatten class $_{p}$ which lack bounded symbols. The lower bound on p is in a certain sense optimal when the symbol of the multiplicative Hankel form is a product of homogeneous linear polynomials.
LA - eng
KW - Hankel forms; infinite-dimensional torus; Schatten class; Nehari's theorem; Dirichlet series
UR - http://eudml.org/doc/285417
ER -