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See detailSome Prevalent Sets in Multifractal Analysis: How Smooth is Almost Every Function in T_p^\alpha(x)
Loosveldt, Laurent UL; Nicolay, Samuel

in Journal of Fourier Analysis and Applications (2022), 28(4),

We present prevalent results concerning generalized versions of the $T_p^\alpha$ spaces, initially introduced by Calderón and Zygmund. We notably show that the logarithmic correction appearing in the ... [more ▼]

We present prevalent results concerning generalized versions of the $T_p^\alpha$ spaces, initially introduced by Calderón and Zygmund. We notably show that the logarithmic correction appearing in the quasi-characterization of such spaces is mandatory for almost every function; it is in particular true for the Hölder spaces, for which the existence of the correction was showed necessary for a specific function. We also show that almost every function from $T_p^α (x0 )$ has α as generalized Hölder exponent at $x_0$. [less ▲]

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See detailAn analogue of Bochner's theorem for Damek-Ricci spaces
Pusti, Sanjoy UL

in Journal of Fourier Analysis and Applications (2013), 19(2), 270284

We characterize the image of radial positive measures $\theta$'s on a harmonic $NA$ group $S$ which satisfies $\int_S\phi_0(x)\,d\theta(x)<\infty$ under the spherical transform, where $\phi_0$ is the ... [more ▼]

We characterize the image of radial positive measures $\theta$'s on a harmonic $NA$ group $S$ which satisfies $\int_S\phi_0(x)\,d\theta(x)<\infty$ under the spherical transform, where $\phi_0$ is the elementary spherical function. [less ▲]

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See detailSpectral Models for Orthonormal Wavelets and Multiresolution Analysis of L2(R)
Gómez-Cubillo, Fernando; Suchanecki, Zdzislaw UL

in Journal of Fourier Analysis and Applications (2011), 17(2), 191-225

Spectral representations of the dilation and translation operators on L2(R) are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid ... [more ▼]

Spectral representations of the dilation and translation operators on L2(R) are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions defined on the functional spectral spaces. The approach is useful for computational purposes. [less ▲]

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