George Benke

A note on weighted Bergman spaces and the Cesáro operator

Abstract. Let B denote the unit ball in C n , and dV (z) normalized Lebesgue measure on B. For α > −1, define dV (z) = (1−|z|)dV (z). Let H(B) denote the space of holomorhic functions on B, and for 0 < p < ∞, let A(dVα) denote L(dVα) ∩ H(B). In this note we characterize A (dVα) as those functions in H(B) whose images under the action of a certain set of differential operators lie in L(dVα). This is valid for 1 ≤ p < ∞. We also show that the Cesàro operator is bounded on A(dVα) for 0 < p < ∞. Analogous results are given for the polydisc.

Smoothness and absolute convergence of Fourier series in compact totally disconnected groups

In this paper we study in the context of compact totally disconnected groups the relationship between the smoothness of a function and its membership in the Fourier algebra GG. Specifically, we define a notion of smoothness which is natural for totally disconnected groups. This in turn leads to the notions of Lipshitz condition and bounded variation. We then give a condition on α which if satisfied implies Lipα(G) ⊂ R(G). On certain groups this condition becomes: α > 12 (Bernsteins theorem). We then give a similar condition on α which if satisfied implies that Lipα(G) ∈ BV(G) ⊂ R(G). On certain groups this condition becomes: α > 0 (Zygmunds theorem). Moreover we show that α > 12 is best possible by showing that Lip12(G) ⊄ R(G).

A spherical Wiener-Plancherel formula

A spherical analogue of Wieners s-function and spherical difference operators are defined for d-dimensional Euclidean space. In this context a spherical Wiener-Plancherel formula is proved.

Wavelet-based analysis of electroencephalogram (EEG) signals for detection and localization of epileptic seizures

A wavelet-based technique WISP is used to discriminate normal brain activity from brain activity during epileptic seizures. The WISP technique is used to exploit the noted difference in frequency content during the normal brain state and the seizure brain state so that detection and localization decisions can be made. An AR-Pole statistic technique is used as a comparative measure to base-line the WISP performance.

Golay–Rudin–Shapiro Polynomials and Phased Arrays

A single-frequency plane wave propagating at speed c in the direction of the unit vector \(\mathbf{N}\) is given by

Adaptively Weighted L 2 -Minimization in Predictive Speech Coding

S(\mathbf{X},t) =\exp i\omega \left (t -\frac{\mathbf{N} \cdot \mathbf{X}} {c} \right ).

Generalized Rudin-Shapiro Systems

(1) Suppose \(\left \{{\mathbf{X}}_{1},\ldots,{\mathbf{X}}_{N}\right \} \subset {\mathbf{R}}^{n}\) is a fixed set of locations, called the array, and \({w}_{1},\ldots,{w}_{N} \subset \mathbf{C}\) is a set of weights. The linear combination