### About biharmonic problem via a spectral approach and decomposition techniques.

Benaissa, Lakhdar, Daili, Noureddine (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

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Benaissa, Lakhdar, Daili, Noureddine (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

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Rachid Sabre (1995)

Applicationes Mathematicae

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We consider a stationary symmetric stable bidimensional process with discrete time, having the spectral representation (1.1). We consider a general case where the spectral measure is assumed to be the sum of an absolutely continuous measure, a discrete measure of finite order and a finite number of absolutely continuous measures on several lines. We estimate the density of the absolutely continuous measure and the density on the lines.

Almira, J.M. (2010)

Annals of Functional Analysis (AFA) [electronic only]

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Manjegani, Seyed Mahmoud (2008)

Banach Journal of Mathematical Analysis [electronic only]

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Ethier, Dillon, Lindberg, Tova, Luttman, Aaron (2010)

Annals of Functional Analysis (AFA) [electronic only]

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Wojciech Hyb (1991)

Annales Polonici Mathematici

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We study the spectral properties of some group of unitary operators in the Hilbert space of square Lebesgue integrable holomorphic functions on a one-dimensional tube (see formula (1)). Applying the Genchev transform ([2], [5]) we prove that this group has continuous simple spectrum (Theorem 4) and that the projection-valued measure for this group has a very explicit form (Theorem 5).

Morales, R., Rojas, E. (2007)

Acta Mathematica Universitatis Comenianae. New Series

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Sababheh, M., Khalil, R. (2009)

The Journal of Nonlinear Sciences and its Applications

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Edmond Granirer (1994)

Colloquium Mathematicae

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Let $C{V}_{p}\left(F\right)$ be the left convolution operators on ${L}^{p}\left(G\right)$ with support included in F and ${M}_{p}\left(F\right)$ denote those which are norm limits of convolution by bounded measures in M(F). Conditions on F are given which insure that $C{V}_{p}\left(F\right)$, $C{V}_{p}\left(F\right)/{M}_{p}\left(F\right)$ and $C{V}_{p}\left(F\right)/W$ are as big as they can be, namely have ${l}^{\infty}$ as a quotient, where the ergodic space W contains, and at times is very big relative to ${M}_{p}\left(F\right)$. Other subspaces of $C{V}_{p}\left(F\right)$ are considered. These improve results of Cowling and Fournier, Price and Edwards, Lust-Piquard, and others.

B. Przeradzki (1992)

Annales Polonici Mathematici

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The existence of bounded solutions for equations x' = A(t)x + r(x,t) is proved, where the linear part is exponentially dichotomic and the nonlinear term r satisfies some weak conditions.

L. Ramsey (1996)

Colloquium Mathematicae

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Lindström, Mikael, Palmberg, Niklas (2007)

Annales Academiae Scientiarum Fennicae. Mathematica

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