### Rényi dimension and Gaussian filtering.

Loring, Terry A. (2007)

The New York Journal of Mathematics [electronic only]

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Loring, Terry A. (2007)

The New York Journal of Mathematics [electronic only]

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František Púchovský (1976)

Mathematica Slovaca

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Qi, Feng, Li, Wei, Guo, Bai-Ni (2006)

Applied Mathematics E-Notes [electronic only]

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Agratini, Octavian (2006)

International Journal of Mathematics and Mathematical Sciences

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Ana Cristina Barroso, José Matias (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the problem of minimizing the energy $$\phantom{\rule{-42.67912pt}{0ex}}E\left(u\right):={\int}_{\Omega}{\left|\nabla u\left(x\right)\right|}^{2}\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x+{\int}_{{S}_{u}\cap \Omega}\left(1+\left|\right[u\left]\right(x\left)\right|\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}{H}^{N-1}\left(x\right)$$ among all functions $u\in SB{V}^{2}\left(\Omega \right)$ for which two level sets $\{u={l}_{i}\}$ have prescribed Lebesgue measure ${\alpha}_{i}$. Subject to this volume constraint the existence of minimizers for $E(\xb7)$ is proved and the asymptotic behaviour of the solutions is investigated.

Nadarajah, Saralees, Kotz, Samuel (2006)

Applied Mathematics E-Notes [electronic only]

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Díaz-Barrero, José Luis (2003)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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Abu-Saris, Raghib M. (2006)

Advances in Difference Equations [electronic only]

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Zhendong Gu, Daochun Sun (2012)

Mathematica Bohemica

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In the paper we obtain that, under some condition, the Rademacher-Dirichlet series or the Steinhaus-Dirichlet series on the whole plane and on the horizontal zone almost surely have the same growth.