Applied and Numerical Harmonic Analysis
Volume 68 / 2015
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11 Result(s)
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Book Series
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Book
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Chapter
The Unreasonable Effectiveness of Haar Frames
Alex Grossmann used to point out the relevance of redundant frame decompositions as opposed to the economical setting supplied by orthonormal bases. We investigate here another unexpected occurrence of the rel...
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Book
New Trends in Applied Harmonic Analysis, Volume 2
Harmonic Analysis, Geometric Measure Theory, and Applications
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Chapter
Multivariate Davenport Series
We consider series of the form ∑a n {n ⋅x}, where n ∈ Z d and {x} is the sawtooth function. They are the natural multivar...
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Chapter
Space-Filling Functions and Davenport Series
In this paper, we study the pointwise Hölder regularity of some spacefilling functions. In particular, we give some general results concerning the pointwise regularity of the Davenport series.
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Chapter and Conference Paper
Wavelet Leaders in Multifractal Analysis
The properties of several multifractal formalisms based on wavelet coefficients are compared from both mathematical and numerical points of view. When it is based directly on wavelet coefficients, the multifra...
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Article
Beyond Besov Spaces Part 1: Distributions of Wavelet Coefficients
We determine which information can be extracted from the distributions of the wavelet coefficients of a function f at each scale, but does not depend on the particular wavelet basis which is chosen. This informat...
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Chapter
Function Spaces Based on Wavelet Expansions
Several extensions of Besov spaces are studied. They take into account the distributions of wavelet coefficients at each scale and the correlations between the positions of the large wavelet coefficients. Thes...
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Article
On a theorem of Ingham
We prove a trigonometric inequality of Ingham’s type for nonharmonic Fourier series when the gap condition between frequencies does not hold any more.
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Article
Old friends revisited: the multifractal nature of some classical functions
We study some explicit functions introduced by Riemann, Jordan, Lévy, Kahane… These functions share the property of having a dense set of discontinuities. We prove that they are examples of multifractal functi...
