Classification and Approximation of Periodic Functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1995
|
| Schriftenreihe: | Mathematics and Its Applications
333 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The chapters are split into sections, which, in turn, are split into subsections enumerated by two numbers: the first stands for the number of the section while the second for the number ofthe subsection itself. The same numeration is used for all kinds of statements and formulas. If we refer to statements or formulas in other chapters, we use triple numeration where the first number stands for the chapter and the other two have the same sense. The results presented in this book were discussed on the seminars at the Institute of Mathematics of Ukrainian Academy ofSciences, at the Steklov Mathematical Institute of the Academy of Sciences of the USSR, at Moscow and Tbilisi State Universities. I am deeply grateful to the heads of these seminars Professors V. K. Dzyadyk, N. P. Korneichuk, S. B. Stechkin, P. L. Ulyanov, and L. V. Zhizhiashvili as well as to the members of these seminars that took an active part in the discussions. INTRODUCTION It is well known for many years that every 21t -periodic summable function f(x) can be associated in a one-to-one manner with its Fourier series (1. 1) Slfl where I It = - f f(t)cosktdt 1t -It and I It - f f(t)sinktdt. 1t -It Therefore, if for approximation of a given function f(·), it is necessary to construct a sequence ofpolynomials Pn ( |
| Beschreibung: | 1 Online-Ressource (X, 366 p) |
| ISBN: | 9789401101158 9789401040556 |
| DOI: | 10.1007/978-94-011-0115-8 |
Internformat
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Datensatz im Suchindex
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| institution | BVB |
| isbn | 9789401101158 9789401040556 |
| language | English |
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| spelling | Stepanets, Alexander I. Verfasser aut Classification and Approximation of Periodic Functions by Alexander I. Stepanets Dordrecht Springer Netherlands 1995 1 Online-Ressource (X, 366 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 333 The chapters are split into sections, which, in turn, are split into subsections enumerated by two numbers: the first stands for the number of the section while the second for the number ofthe subsection itself. The same numeration is used for all kinds of statements and formulas. If we refer to statements or formulas in other chapters, we use triple numeration where the first number stands for the chapter and the other two have the same sense. The results presented in this book were discussed on the seminars at the Institute of Mathematics of Ukrainian Academy ofSciences, at the Steklov Mathematical Institute of the Academy of Sciences of the USSR, at Moscow and Tbilisi State Universities. I am deeply grateful to the heads of these seminars Professors V. K. Dzyadyk, N. P. Korneichuk, S. B. Stechkin, P. L. Ulyanov, and L. V. Zhizhiashvili as well as to the members of these seminars that took an active part in the discussions. INTRODUCTION It is well known for many years that every 21t -periodic summable function f(x) can be associated in a one-to-one manner with its Fourier series (1. 1) Slfl where I It = - f f(t)cosktdt 1t -It and I It - f f(t)sinktdt. 1t -It Therefore, if for approximation of a given function f(·), it is necessary to construct a sequence ofpolynomials Pn ( Mathematics Harmonic analysis Fourier analysis Sequences (Mathematics) Sequences, Series, Summability Approximations and Expansions Fourier Analysis Abstract Harmonic Analysis Mathematik Approximation (DE-588)4002498-2 gnd rswk-swf Periodische Funktion (DE-588)4224901-6 gnd rswk-swf Klassifikation (DE-588)4030958-7 gnd rswk-swf Periodische Funktion (DE-588)4224901-6 s Approximation (DE-588)4002498-2 s Klassifikation (DE-588)4030958-7 s 1\p DE-604 Mathematics and Its Applications 333 (DE-604)BV008163334 333 https://doi.org/10.1007/978-94-011-0115-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stepanets, Alexander I. Classification and Approximation of Periodic Functions Mathematics and Its Applications Mathematics Harmonic analysis Fourier analysis Sequences (Mathematics) Sequences, Series, Summability Approximations and Expansions Fourier Analysis Abstract Harmonic Analysis Mathematik Approximation (DE-588)4002498-2 gnd Periodische Funktion (DE-588)4224901-6 gnd Klassifikation (DE-588)4030958-7 gnd |
| subject_GND | (DE-588)4002498-2 (DE-588)4224901-6 (DE-588)4030958-7 |
| title | Classification and Approximation of Periodic Functions |
| title_auth | Classification and Approximation of Periodic Functions |
| title_exact_search | Classification and Approximation of Periodic Functions |
| title_full | Classification and Approximation of Periodic Functions by Alexander I. Stepanets |
| title_fullStr | Classification and Approximation of Periodic Functions by Alexander I. Stepanets |
| title_full_unstemmed | Classification and Approximation of Periodic Functions by Alexander I. Stepanets |
| title_short | Classification and Approximation of Periodic Functions |
| title_sort | classification and approximation of periodic functions |
| topic | Mathematics Harmonic analysis Fourier analysis Sequences (Mathematics) Sequences, Series, Summability Approximations and Expansions Fourier Analysis Abstract Harmonic Analysis Mathematik Approximation (DE-588)4002498-2 gnd Periodische Funktion (DE-588)4224901-6 gnd Klassifikation (DE-588)4030958-7 gnd |
| topic_facet | Mathematics Harmonic analysis Fourier analysis Sequences (Mathematics) Sequences, Series, Summability Approximations and Expansions Fourier Analysis Abstract Harmonic Analysis Mathematik Approximation Periodische Funktion Klassifikation |
| url | https://doi.org/10.1007/978-94-011-0115-8 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT stepanetsalexanderi classificationandapproximationofperiodicfunctions |