## The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet ApproximationsThis is the first book dedicated to covering the basic elements of the Gibbs phenomenon as it appears in various applications where functions with jump discontinuities are represented. It is presented with detailed analysis and illustrations combined with historical information. The author covers the appearance of the Gibbs phenomenon in Fourier analysis, orthogonal expansions, integral transforms, splines and wavelet approximations. Methods of reducing, or filtering out, such phenomena that cover all the above function representations are also addressed. The book includes a thorough bibliography of some 350 references. Audience: The work is intended as an introduction for engineering and scientific practitioners in the fields where this phenomenon may appear in their use of various function representations. It may also be used by qualified students. |

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### Contents

IV | 1 |

V | 3 |

VI | 12 |

VIII | 16 |

IX | 26 |

X | 28 |

XI | 31 |

XII | 34 |

XXXIX | 137 |

XL | 140 |

XLI | 148 |

XLII | 150 |

XLIII | 155 |

XLIV | 156 |

XLVI | 157 |

XLVII | 159 |

XIII | 37 |

XIV | 38 |

XV | 40 |

XVI | 43 |

XVII | 44 |

XVIII | 45 |

XIX | 55 |

XX | 56 |

XXI | 57 |

XXII | 67 |

XXIII | 73 |

XXIV | 78 |

XXV | 80 |

XXVI | 83 |

XXVII | 100 |

XXVIII | 107 |

XXIX | 109 |

XXX | 110 |

XXXI | 112 |

XXXII | 119 |

XXXIII | 122 |

XXXV | 125 |

XXXVI | 127 |

XXXVII | 130 |

XXXVIII | 131 |

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### References from web pages

Mathematics and Its Applications

The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations Abdul J. Jerri Clarkson University KLUWER ACADEMIC PUBLISHERS ...

www.clarkson.edu/ ~jerria/ solnman/ gibbs.html

Gibbs' phenomenon and arclength

The Gibbs phenomenon in Fourier analysis, splines and wavelet approximations, Kluwer Academic. Publishers, Dordrecht. [5l Kelly, S+E. (1996); ...

www.springerlink.com/ index/ UM75863J21KKH377.pdf

Hybrid sampling series associated with orthogonal wavelets and **...**

aj Jerri, The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations , Kluwer Academic, Boston, 1998. 5 5. se Kelly, ma Kon and la Raphael ...

portal.acm.org/ citation.cfm?id=864538.864554

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The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations · The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations ...

www.libreriauniversitaria.it/ books-author_abdul+j+jerri-abdul+j+jerri.htm