Time Frequency Localization of Trigonometric Hermite Operators
نویسنده
چکیده
In this paper, localization properties of trigonometric polynomial Hermite operators are discussed. In particular, time frequency uncertainty and operator norms are compared for the diierent types of fundamental interpolants which serve as scaling functions for a trigono-metric multiresolution analysis. x1. Introduction Recently, several diierent approaches to periodic multiresolution analyses have been presented. For example, periodic scaling functions and wavelets are discussed by Narcowich and Ward 3] who investigate their time frequency behaviour in terms of an uncertainty principle for periodic functions due to Breitenberger 1]. The periodic basis functions in 3] possess an uncertainty product of O(p n) for increasing dimension n of the corresponding spaces. On the other hand, uniformly bounded uncertainty products are computed by Selig 6] for trigonometric fundamental Lagrange interpolants based on de la Vall ee Poussin means. A multiresolution analysis generated by two diierent types of scaling functions and wavelets, namely fundamental trigonometric Hermite interpolants, is investigated in 5]. One of these scaling functions is a Fej er kernel, while the other is a conjugate Dirichlet kernel. In this paper, we explain the diierent behaviour of these two types of functions with respect to their localization properties. This includes the computation of the time frequency uncertainty as well as the operator norms. Let us remark here that similar diierences also occur for the de la Vall ee Poussin and Fourier type Lagrange interpolants which are described in 4].
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