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

• Autorzy: Boris Paneah
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 37
• Numer: 1
• Strony: 331-335

Daty

wydano

1996

Twórcy

autor

Boris Paneah

• Department of Mathematics, Technion, 32000, Haifa, Israel