The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations
By: by Abdul J. Jerri
Series: Mathematics and Its Applications -- 446; Mathematics and Its Applications -- 446
Publisher: Springer US; Imprint: Springer
Published: 1998
Place of publication: Boston, MA
Language: eng
Format: [electronic resource] /
Number of pages: 364
ISBN-13: 9781475728477
Subjects: Harmonic analysis; Mathematics; Fourier analysis; Sequences (Mathematics); Computer science
Description: This 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.