Frames associated with expansive matrix dilations.

Kwok-Pun Ho

Displaying similar documents to “Frames associated with expansive matrix dilations.”

Some Marginal Densities of the Wishart Distribution Някои маргинални плътности на разпределението на Уишарт

Veleva, Evelina (2012)

Union of Bulgarian Mathematicians

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Евелина Илиева Велева - Разпределението на Уишарт се среща в практиката като разпределението на извадъчната ковариационна матрица за наблюдения над многомерно нормално разпределение. Изведени са някои маргинални плътности, получени чрез интегриране на плътността на Уишарт разпределението. Доказани са необходими и достатъчни условия за положителна определеност на една матрица, които дават нужните граници за интегрирането. Wishart distribution arises as the distribution of...

Topological degree, Jacobian determinants and relaxation

Irene Fonseca, Nicola Fusco, Paolo Marcellini (2005)

Bollettino dell'Unione Matematica Italiana

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A characterization of the total variation $T V (u, Ω)$ of the Jacobian determinant $det D u$ is obtained for some classes of functions $u : Ω \to R^{n}$ outside the traditional regularity space $W^{1, n} (Ω; R^{n})$ . In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity $x_{0} \in Ω$ . Relations between $T V (u, Ω)$ and the distributional determinant $Det D u$ are established, and an integral representation is obtained for the relaxed energy of certain polyconvex functionals at maps $u \in W^{1, p} (Ω; R^{n}) \cap W^{1, \infty} (Ω \{x_{0}\}; R^{n})$ . ...

Translational averaging for completeness, characterization and oversampling of wavelets.

Richard S. Laugesen (2002)

Collectanea Mathematica

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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,...