JEDNOSTKA NAUKOWA KATEGORII A+

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

Tom 37 / 1996

Boris Paneah Banach Center Publications 37 (1996), 331-335 DOI: 10.4064/-37-1-331-335

Streszczenie

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.

Autorzy

  • Boris Paneah

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek