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Theoretical aspects of a multiscale analysis of the eigenoscillations of the Earth.

Volker Michel (2003)

Revista Matemática Complutense

The elastic behaviour of the Earth, including its eigenoscillations, is usually described by the Cauchy-Navier equation. Using a standard approach in seismology we apply the Helmholtz decomposition theorem to transform the Fourier transformed Cauchy-Navier equation into two non-coupled Helmholtz equations and then derive sequences of fundamental solutions for this pair of equations using the Mie representation. Those solutions are denoted by the Hansen vectors Ln,j, Mn,j, and Nn,j in geophysics....

Topological Dichotomy and Unconditional Convergence

Lefevre, Pascal (1999)

Serdica Mathematical Journal

In this paper, we give a criterion for unconditional convergence with respect to some summability methods, dealing with the topological size of the set of choices of sign providing convergence. We obtain similar results for boundedness. In particular, quasi-sure unconditional convergence implies unconditional convergence.

Tractable embeddings of Besov spaces into Zygmund spaces

Hans Triebel (2011)

Banach Center Publications

The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on n-dimensional cubes into Zygmund spaces. This can be expressed in terms of tractability envelopes.

Transformée en paquets d'ondelettes des signaux stationnaires: comportement asymptotique des densités spectrales.

Loïc Hervé (1996)

Revista Matemática Iberoamericana

We consider quadrature mirror filters, and the associated wavelet packet transform. Let X = {Xn}n∈Z be a stationary signal which has a continuous spectral density f. We prove that the 2n signals obtained from X by n iterations of the transform converge to white noises when n → +∞. If f is holderian, the convergence rate is exponential.

Translational averaging for completeness, characterization and oversampling of wavelets.

Richard S. Laugesen (2002)

Collectanea Mathematica

The single underlying method of averaging the wavelet functional over translates yields first a new completeness criterion for orthonormal wavelet systems, and then a unified treatment of known results on characterization of wavelets on the Fourier transform side, on preservation of frame bounds by oversampling, and on equivalence of affine and quasiaffine frames. The method applies to multiwavelet systems in all dimensions, to dilation matrices that are in some cases not expanding, and to dual...

Transplantation operators and Cesàro operators for the Hankel transform

Yuichi Kanjin (2006)

Studia Mathematica

The transplantation operators for the Hankel transform are considered. We prove that the transplantation operator maps an integrable function under certain conditions to an integrable function. As an application, we obtain the L¹-boundedness and H¹-boundedness of Cesàro operators for the Hankel transform.

Triebel-Lizorkin spaces for Hermite expansions

Jay Epperson (1995)

Studia Mathematica

This paper develops some Littlewood-Paley theory for Hermite expansions. The main result is that certain analogues of Triebel-Lizorkin spaces are well-defined in the context of Hermite expansions.

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