arXiv subjects
Publications and source records attributed to E. Lebedeva.
In this paper we introduce a notion of a directional uncertainty product for multivariate periodic functions. It measures a localization of a function along a particular direction. We study properties of the uncertainty product and give an example of well localized multivariate periodic Parseval wavelet frames.
A directional time-frequency localization measure for functions defined on the $d$-dimensional Euclidean space is introduced. A connection between this measure and its periodic counterpart is established. For a class of functions, an optimization problem for finding the optimal direction, along which a function is best or worst localized, is solved.
Ordinary and partial differential equation for unknown functions defined on the Cantor dyadic group are studied. We consider two types of equations: related to the Gibbs derivatives and to the fractional modified Gibbs derivatives (or pseudo differential-operators). We find solutions in classes of distributions and study under what assumptions these solutions are regular functions with some "good" properties.