Browsing by Subject "Uncertainty principle"

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Open Access
Uncertainty principles in holomorphic function spaces on the unit ball
(Cambridge University Press, 2023-07-10) Kaptanoğlu, Hakkı Turgay
On all Bergman–Besov Hilbert spaces on the unit disk, we find self-adjoint weighted shift operators that are differential operators of half-order whose commutators are the identity, thereby obtaining uncertainty relations in these spaces. We also obtain joint average uncertainty relations for pairs of commuting tuples of operators on the same spaces defined on the unit ball. We further identify functions that yield equality in some uncertainty inequalities.
Open Access
Universal lower bound for finite-sample reconstruction error and ıts relation to prolate spheroidal functions
(Institute of Electrical and Electronics Engineers, 2018) Gülcü, T. C.; Özaktaş, Haldun M.
We consider the problem of representing a finite-energy signal with a finite number of samples. When the signal is interpolated via sinc function from the samples, there will be a certain reconstruction error since only a finite number of samples are used. Without making any additional assumptions, we derive a lower bound for this error. This error bound depends on the number of samples but nothing else, and is thus represented as a universal curve of error versus number of samples. Furthermore, the existence of a function that achieves the bound shows that this is the tightest such bound possible.