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Harmonic analysis of the space BV.

Albert Cohen, Wolfgang Dahmen, Ingrid Daubechies, Ronald DeVore (2003)

Revista Matemática Iberoamericana

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-l1 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...

Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms.

Aline Bonami, Demange, Bruno, Jaming, Philippe (2003)

Revista Matemática Iberoamericana

We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on Rd which may be written as P(x)exp(-(Ax,x)), with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f(x)f(y). We then obtain similar results for the windowed Fourier transform (also known, up to elementary changes of functions, as the radar ambiguity function or the Wigner transform). We complete the paper with...

How smooth is almost every function in a Sobolev space?

Aurélia Fraysse, Stéphane Jaffard (2006)

Revista Matemática Iberoamericana

We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.

Inequivalence of Wavelet Systems in L ₁ ( ℝ d ) and B V ( ℝ d )

Paweł Bechler (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

Theorems stating sufficient conditions for the inequivalence of the d-variate Haar wavelet system and another wavelet system in the spaces L ₁ ( ℝ d ) and B V ( ℝ d ) are proved. These results are used to show that the Strömberg wavelet system and the system of continuous Daubechies wavelets with minimal supports are not equivalent to the Haar system in these spaces. A theorem stating that some systems of smooth Daubechies wavelets are not equivalent to the Haar system in L ₁ ( ℝ d ) is also shown.

Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets

Fitouhi, Ahmed, Bettaibi, Néji, Binous, Wafa (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 42A38, 42C40, 33D15, 33D60This paper aims to study the q-wavelets and the continuous q-wavelet transforms, associated with the q-Bessel operator for a fixed q ∈]0, 1[. Using the q-Riemann-Liouville and the q-Weyl transforms, we give some relations between the continuous q-wavelet transform, studied in [3], and the continuous q-wavelet transform associated with the q-Bessel operator, and we deduce formulas which give the inverse operators of the q-Riemann-Liouville and...

Isometric tight frames.

Reams, Robert, Waldron, Shayne (2002)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Currently displaying 121 – 140 of 324