Equivalent norms in some spaces of analytic functions and the uncertainty principle

@article{Paneah1996,
abstract = {The main object of this work is to describe such weight functions w(t) that for all elements $f ∈ L_\{p,Ω\}$ the estimate $∥ wf∥_p ≥K(Ω)∥ f∥_p$ is valid with a constant K(Ω), which does not depend on f and it grows to infinity when the domain Ω shrinks, i.e. deforms into a lower dimensional convex set $Ω_∞$. In one-dimensional case means that $K(σ):= K(Ω_σ) → ∞$ as σ → 0. It should be noted that in the framework of the signal transmission problem such estimates describe a signal’s behavior under the influence of detection and amplification. This work contains some results of the above-mentioned type which I presented at the Banach Centre in the Summer of 1994. Some of these results had been published earlier, some are new ones.},
author = {Paneah, Boris},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {331-335},
title = {Equivalent norms in some spaces of analytic functions and the uncertainty principle},
url = {http://eudml.org/doc/208610},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Paneah, Boris
TI - Equivalent norms in some spaces of analytic functions and the uncertainty principle
JO - Banach Center Publications
PY - 1996
VL - 37
IS - 1
SP - 331
EP - 335
AB - The main object of this work is to describe such weight functions w(t) that for all elements $f ∈ L_{p,Ω}$ the estimate $∥ wf∥_p ≥K(Ω)∥ f∥_p$ is valid with a constant K(Ω), which does not depend on f and it grows to infinity when the domain Ω shrinks, i.e. deforms into a lower dimensional convex set $Ω_∞$. In one-dimensional case means that $K(σ):= K(Ω_σ) → ∞$ as σ → 0. It should be noted that in the framework of the signal transmission problem such estimates describe a signal’s behavior under the influence of detection and amplification. This work contains some results of the above-mentioned type which I presented at the Banach Centre in the Summer of 1994. Some of these results had been published earlier, some are new ones.
LA - eng
UR - http://eudml.org/doc/208610
ER -