## New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing, and Multifractal AnalysisAkram Aldroubi, Carlos Cabrelli, Stephane Jaffard, Ursula Molter This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and cover both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics. |

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### Contents

1 | |

2 Multifractal Analysis and Wavelets | 19 |

3 An Introduction to Mandelbrot Cascades | 67 |

4 LebesgueType Inequalities for Greedy Approximation | 106 |

5 Results on Nonlinear Approximation for Wavelet Bases in Weighted Function Spaces | 145 |

6 Consequences of the MarcusSpielmanSrivastava Solution of the KadisonSinger Problem | 190 |

7 Model Sets and New Versions of Shannon Sampling Theorem | 215 |

8 Stylometry and Mathematical Study of Authorship | 280 |

9 Thoughts on Numerical and Conceptual Harmonic Analysis | 301 |

Applied and Numerical Harmonic Analysis 74 volumes | 331 |

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applied Argentina assume Banach space Besov spaces Borel bounded Cantor measure Cantor set chrono-divide compact compactly supported constant continuous function convergence Corollary cubes defined Definition Delone set denote Dirac dyadic equivalent example exists Feichtinger Conjecture fi}ieſ Fourier Analysis Fourier coefficients Fourier transform frame frequencies function f g-a-p function g-a-p measure given Greedy Algorithm Harmonic Analysis Hausdorff dimension Hence Hilbert space implies interval ISBN Kadison-Singer Problem lattice Lebesgue Lebesgue-type inequalities Lemma LP(w Mandelbrot cascades Math mathematical model set multifractal analysis multifractal spectrum notations obtain Orlicz spaces parameter Paving Conjecture periodic function periodic measure pointwise polynomial proof of Theorem properties Proposition prove quasicrystal real number Red Chamber result Riemann integrable Riesz sampling satisfies Section self-similar sequence signal stylometry subset theory trigonometric V.N. Temlyakov vector wavelet coefficients wavelet series WCGA