Trigonometric Fourier Series and Their Conjugates:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1996
|
| Schriftenreihe: | Mathematics and Its Applications
372 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Research in the theory of trigonometric series has been carried out for over two centuries. The results obtained have greatly influenced various fields of mathematics, mechanics, and physics. Nowadays, the theory of simple trigonometric series has been developed fully enough (we will only mention the monographs by Zygmund [15, 16] and Bari [2]). The achievements in the theory of multiple trigonometric series look rather modest as compared to those in the one-dimensional case though multiple trigonometric series seem to be a natural, interesting and promising object of investigation. We should say, however, that the past few decades have seen a more intensive development of the theory in this field. To form an idea about the theory of multiple trigonometric series, the reader can refer to the surveys by Shapiro [1], Zhizhiashvili [16], [46], Golubov [1], D'yachenko [3]. As to monographs on this topic, only that ofYanushauskas [1] is known to me. This book covers several aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions; convergence (pointwise and in the LP-norm, p > 0) of Fourier series and their conjugates, as well as their summability by the Cesaro (C,a), a> -1, and Abel-Poisson methods; approximating properties of Cesaro means of Fourier series and their conjugates |
| Beschreibung: | 1 Online-Ressource (XII, 308 p) |
| ISBN: | 9789400902831 9789401066129 |
| DOI: | 10.1007/978-94-009-0283-1 |
Internformat
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| 500 | |a Research in the theory of trigonometric series has been carried out for over two centuries. The results obtained have greatly influenced various fields of mathematics, mechanics, and physics. Nowadays, the theory of simple trigonometric series has been developed fully enough (we will only mention the monographs by Zygmund [15, 16] and Bari [2]). The achievements in the theory of multiple trigonometric series look rather modest as compared to those in the one-dimensional case though multiple trigonometric series seem to be a natural, interesting and promising object of investigation. We should say, however, that the past few decades have seen a more intensive development of the theory in this field. To form an idea about the theory of multiple trigonometric series, the reader can refer to the surveys by Shapiro [1], Zhizhiashvili [16], [46], Golubov [1], D'yachenko [3]. As to monographs on this topic, only that ofYanushauskas [1] is known to me. This book covers several aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions; convergence (pointwise and in the LP-norm, p > 0) of Fourier series and their conjugates, as well as their summability by the Cesaro (C,a), a> -1, and Abel-Poisson methods; approximating properties of Cesaro means of Fourier series and their conjugates | ||
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Datensatz im Suchindex
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| author | Zhizhiashvili, Levan |
| author_facet | Zhizhiashvili, Levan |
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| dewey-full | 515.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.2433 |
| dewey-search | 515.2433 |
| dewey-sort | 3515.2433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-009-0283-1 |
| format | Electronic eBook |
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| id | DE-604.BV042423633 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9789400902831 9789401066129 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859050 |
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| physical | 1 Online-Ressource (XII, 308 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1996 |
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| publisher | Springer Netherlands |
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| series2 | Mathematics and Its Applications |
| spelling | Zhizhiashvili, Levan Verfasser aut Trigonometric Fourier Series and Their Conjugates by Levan Zhizhiashvili Dordrecht Springer Netherlands 1996 1 Online-Ressource (XII, 308 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 372 Research in the theory of trigonometric series has been carried out for over two centuries. The results obtained have greatly influenced various fields of mathematics, mechanics, and physics. Nowadays, the theory of simple trigonometric series has been developed fully enough (we will only mention the monographs by Zygmund [15, 16] and Bari [2]). The achievements in the theory of multiple trigonometric series look rather modest as compared to those in the one-dimensional case though multiple trigonometric series seem to be a natural, interesting and promising object of investigation. We should say, however, that the past few decades have seen a more intensive development of the theory in this field. To form an idea about the theory of multiple trigonometric series, the reader can refer to the surveys by Shapiro [1], Zhizhiashvili [16], [46], Golubov [1], D'yachenko [3]. As to monographs on this topic, only that ofYanushauskas [1] is known to me. This book covers several aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions; convergence (pointwise and in the LP-norm, p > 0) of Fourier series and their conjugates, as well as their summability by the Cesaro (C,a), a> -1, and Abel-Poisson methods; approximating properties of Cesaro means of Fourier series and their conjugates Mathematics Fourier analysis Integral Transforms Sequences (Mathematics) Fourier Analysis Approximations and Expansions Integral Transforms, Operational Calculus Sequences, Series, Summability Real Functions Mathematik Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 s 1\p DE-604 https://doi.org/10.1007/978-94-009-0283-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zhizhiashvili, Levan Trigonometric Fourier Series and Their Conjugates Mathematics Fourier analysis Integral Transforms Sequences (Mathematics) Fourier Analysis Approximations and Expansions Integral Transforms, Operational Calculus Sequences, Series, Summability Real Functions Mathematik Fourier-Reihe (DE-588)4155109-6 gnd |
| subject_GND | (DE-588)4155109-6 |
| title | Trigonometric Fourier Series and Their Conjugates |
| title_auth | Trigonometric Fourier Series and Their Conjugates |
| title_exact_search | Trigonometric Fourier Series and Their Conjugates |
| title_full | Trigonometric Fourier Series and Their Conjugates by Levan Zhizhiashvili |
| title_fullStr | Trigonometric Fourier Series and Their Conjugates by Levan Zhizhiashvili |
| title_full_unstemmed | Trigonometric Fourier Series and Their Conjugates by Levan Zhizhiashvili |
| title_short | Trigonometric Fourier Series and Their Conjugates |
| title_sort | trigonometric fourier series and their conjugates |
| topic | Mathematics Fourier analysis Integral Transforms Sequences (Mathematics) Fourier Analysis Approximations and Expansions Integral Transforms, Operational Calculus Sequences, Series, Summability Real Functions Mathematik Fourier-Reihe (DE-588)4155109-6 gnd |
| topic_facet | Mathematics Fourier analysis Integral Transforms Sequences (Mathematics) Fourier Analysis Approximations and Expansions Integral Transforms, Operational Calculus Sequences, Series, Summability Real Functions Mathematik Fourier-Reihe |
| url | https://doi.org/10.1007/978-94-009-0283-1 |
| work_keys_str_mv | AT zhizhiashvililevan trigonometricfourierseriesandtheirconjugates |