Sandor Fridli

Hardy Spaces Generated by an Integrability Condition

S. A. Telyakovskii (1964, Izv. Akad. Nauk. SSR. Ser. Mat.28, 1209-1236) proved an integrability condition for cosine series. No condition superior to that has been given so far. In this paper we identify the atomic structure of the Hardy type space that can be associated with this condition. As a consequence, we conclude that Telyakovskiis condition is equivalent to certain Sidon type inequalities. Then on the basis of this equivalence we show how the atomic technique can be used to extend Telyakovskiis condition to several systems, including Walsh series and integrals, in a uniform way.

Heartbeat Classification of ECG Signals Using Rational Function Systems.

The main idea of this paper is to show that rational orthogonal function systems, called Malmquist-Takenaka (MT) systems can effectively be used for ECG heartbeat classification. The idea behind using these systems is the adaptive nature of them. Then the constructed feature vector consists of two main parts, called dynamic and morphological parameters. The latter ones contain the coefficients of the orthogonal projection with respect to the MT systems. Then Support Vector Machine algorithm was used for classifying the heartbeats into the usual 16 arrhythmia classes. The comparison test were performed on the MIT-BIH arrhythmia database. The results show that our algorithm outperforms the previous ones in many respects.

Dyadic Derivative, Summation, Approximation

The “Hungarian school” has played an active role in the development of the theory of dyadic derivative, in particular in exploring its properties related to the fundamental theorem, right from the beginning. New concepts and techniques have emerged on which summaries can be found in the relevant chapters of the monographes [SchWadSim90], [Wei02]. In this survey paper we present the results on the fundamental theory of dyadic derivative, and their effect on the solutions of problems regarding to summation, approximation of Walsh–Fourier series, Cesaro operators etc., by focusing on the involvement of the Hungarian mathematicians. We note, that in the last ten years intensive research have been carried on in Russia (see e.g. [Gol13a*], [GolVol13a*]) by taking the generalized concept, due to Onneweer [Onn13*], instead of the original concept of the dyadic derivative. We think that these results augment each other well by showing the similarities and the differences between the two approaches. The latest results for the multidimension case are summed up in the paper ofWeisz [Wei13*] in this volume. In general the * sign in the citations indicate that the paper, or its copy can be found in this volume.

Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations

The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible. The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area.