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

Paneah, Boris. "Equivalent norms in some spaces of analytic functions and the uncertainty principle." Banach Center Publications 37.1 (1996): 331-335. <http://eudml.org/doc/208610>.

@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 -