Szczegóły publikacji
Opis bibliograficzny
Foundations of the theory of strongly periodically correlated fields over $Z^{2}$ / Anna E. DUDEK, Dominique Dehay, Harry Hurd, Andrzej Makagon // W: Nonstationary systems: theory and applications : contributions to the 13th workshop on Nonstationary systems and their applications : February 3–5, 2020, Grodek nad Dunajcem, Poland / eds. Fakher Chaari, [et al.]. — Cham : Springer Nature Switzerland, cop. 2022. — (Applied Condition Monitoring ; ISSN 2363-698X ; vol. 18). — ISBN: 978-3-030-82191-3; e-ISBN: 978-3-030-82110-4. — S. 127–144. — Bibliogr. s. 143–144, Abstr. — Publikacja dostępna online od: 2021-07-22
Autorzy (4)
- AGHDudek Anna
- Dehay Dominique
- Hurd Harry
- Makagon Andrzej
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 135364 |
|---|---|
| Data dodania do BaDAP | 2021-07-27 |
| DOI | 10.1007/978-3-030-82110-4_7 |
| Rok publikacji | 2022 |
| Typ publikacji | materiały konferencyjne (aut.) |
| Otwarty dostęp |  |
| Wydawca | Springer |
| Czasopismo/seria | Applied Condition Monitoring |
Abstract
The aim of this paper is to provide readers with basic concepts and techniques for analysis of strongly periodically correlated fields (SCF) over Z2 . We show that every SCF over Z2 can be transformed into a coordinate-wise SCF (Fact 3.1) studied in [13]. The main result of the paper however is a specific decomposition of a strongly periodically correlated field (Theorem 4.1) which was not available for coordinate-wise SCFs. As consequences of the latter we obtain a description and an easy proof of existence of the spectral measures of an SCF (Theorem 5.1) as well as a functional description of an absolutely continuous SCF (Theorem 6.1). Most of the facts are explained in details and proved, with an exception of the proof of Theorem 6.1, which was too long for this publication and is left for a forthcoming paper.
