Harmonic analysis of the space BV.
TLDR
In this paper, it was shown that if a function f is in BV, its coefficient sequence in a normalized wavelet basis satisfies a class of weak-� 1 type estimates.Abstract:
We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is “almost” characterized by wavelet expansions in the following sense: if a function f is in BV, its coefficient sequence in a BV normalized wavelet basis satisfies a class of weak-� 1 type estimates. These weak estimates can be employed to prove many interesting results. We use them to identify the interpolation spaces between BV and Sobolev or Besov spaces, and to derive new Gagliardo-Nirenberg-type inequalities. 1. Background and main resultsread more
Citations
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Iterative Regularization and Nonlinear Inverse Scale Space Applied to Wavelet-Based Denoising
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References
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Book
Ten lectures on wavelets
TL;DR: This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.
Journal ArticleDOI
Ten Lectures on Wavelets
TL;DR: In this article, the regularity of compactly supported wavelets and symmetry of wavelet bases are discussed. But the authors focus on the orthonormal bases of wavelets, rather than the continuous wavelet transform.
Book
Measure theory and fine properties of functions
TL;DR: In this article, the authors define and define elementary properties of BV functions, including the following: Sobolev Inequalities Compactness Capacity Quasicontinuity Precise Representations of Soboleve Functions Differentiability on Lines BV Function Differentiability and Structure Theorem Approximation and Compactness Traces Extensions Coarea Formula for BV Functions isoperimetric inequalities The Reduced Boundary The Measure Theoretic Boundary Gauss-Green Theorem Pointwise Properties this article.
Ondelettes et operateurs I
TL;DR: In this paper, the authors propose a new theory of Fourier, which tend to remplacer dans certains cases l'analyse de Fourier and tend to re-applique a divers secteurs de la science and de la technologie comme la turbulence, le traitement du signal, l'acoustique musicale, etc.
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