03638nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001800153072001700171072002300188082001700211245020600228264004600434300004600480336002600526337002600552338003600578347002400614490004400638505034800682520164901030650001702679650002302696650002202719650001302741650001702754650002202771650003202793650004102825650005702866700003202923700003102955710003402986773002003020776003603040830004403076856004803120978-0-8176-4891-6DE-He21320180115171441.0cr nn 008mamaa100301s2010 xxu| s |||| 0|eng d a97808176489167 a10.1007/978-0-8176-4891-62doi 4aQA403.5-404.5 7aPBKF2bicssc 7aMAT0340002bisacsh04a515.243322310aFour Short Courses on Harmonic Analysish[electronic resource] :bWavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis /cedited by Brigitte Forster, Peter Massopust. 1aBoston, MA :bBirkhäuser Boston,c2010. aXVIII, 249 p. 36 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aApplied and Numerical Harmonic Analysis0 aIntroduction: Mathematical Aspects of Time-Frequency Analysis -- B-Spline Generated Frames -- Continuous and Discrete Reproducing Systems That Arise from Translations. Theory and Applications of Composite Wavelets -- Wavelets on the Sphere -- Wiener’s Lemma: Theme and Variations. An Introduction to Spectral Invariance and Its Applications. aThis state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field, including cosmic microwave background analysis, human cortex image denoising, and wireless communication. The work is the first one that combines spline theory (from a numerical or approximation-theoretical view), wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn. Written by internationally renowned mathematicians, the interdisciplinary chapters are expository by design, enabling the reader to understand the theory behind modern image and signal processing methodologies. The main emphasis throughout the book is on the interdependence of the four modern research directions covered. Each chapter ends with exercises that allow for a more in-depth understanding of the material and are intended to stimulate the reader toward further research. A comprehensive index completes the work. Topics covered: * Frames and bases in mathematics and engineering * Wavelets with composite dilations and their applications * Wavelets on the sphere and their applications * Wiener's Lemma: theme and variations Four Short Courses on Harmonic Analysis is intended as a graduate-level textbook for courses or seminars on harmonic analysis and its applications. The work is also an excellent reference or self-study guide for researchers and practitioners with diverse mathematical backgrounds working in different fields such as pure and applied mathematics, image and signal processing engineering, mathematical physics, and communication theory. 0aMathematics. 0aHarmonic analysis. 0aFourier analysis. 0aPhysics.14aMathematics.24aFourier Analysis.24aAbstract Harmonic Analysis.24aSignal, Image and Speech Processing.24aTheoretical, Mathematical and Computational Physics.1 aForster, Brigitte.eeditor.1 aMassopust, Peter.eeditor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817648909 0aApplied and Numerical Harmonic Analysis40uhttp://dx.doi.org/10.1007/978-0-8176-4891-6