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Abstract
Given a periodic function f , we study the almost everywhere and norm convergence of series∑∞ k=1 c k f (kx). As the classical theory shows, the behavior of such series is determined by a combination of analytic and number theoretic factors, but precise results exist only in a few special cases. In this paper, we use connections with orthogonal function theory and greatest common divisor sums to prove several new results and improve old ones, and also to simplify and unify the theory.
| Originalsprache | englisch |
|---|---|
| Seiten (von - bis) | 25-52 |
| Fachzeitschrift | The Quarterly Journal of Mathematics |
| Jahrgang | 65 |
| Ausgabenummer | 1 |
| DOIs | |
| Publikationsstatus | Veröffentlicht - 2014 |
Fields of Expertise
- Information, Communication & Computing
Treatment code (Nähere Zuordnung)
- Basic - Fundamental (Grundlagenforschung)
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Untersuchen Sie die Forschungsthemen von „On series of dilated functions“. Zusammen bilden sie einen einzigartigen Fingerprint.Projekte
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Analytic Combinatorics: Analytic Combinatorics and Probabilistic Number Theory
Wagner, S., Madritsch, M., Aistleitner, C., Barat, G., Thuswaldner, J., Grabner, P., Van De Woestijne, C. E., Heuberger, C., Brauchart, J., Berkes, I., Filipin, A., Zeiner, M. & Tichy, R.
1/01/06 → 31/07/12
Projekt: Forschungsprojekt