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

Banach Center Publications (1996)

- Volume: 37, Issue: 1, page 331-335
- ISSN: 0137-6934

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topPaneah, 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 -

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