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Observability properties of a semi-discrete 1d wave equation derived from a mixed finite element method on nonuniform meshes

Sylvain Ervedoza (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The goal of this article is to analyze the observability properties for a space semi-discrete approximation scheme derived from a mixed finite element method of the 1d wave equation on nonuniform meshes. More precisely, we prove that observability properties hold uniformly with respect to the mesh-size under some assumptions, which, roughly, measures the lack of uniformity of the meshes, thus extending the work [Castro and Micu, Numer. Math.102 (2006) 413–462] to nonuniform meshes. Our results...

On a binary relation between normal operators

Takateru Okayasu, Jan Stochel, Yasunori Ueda (2011)

Studia Mathematica

The main goal of this paper is to clarify the antisymmetric nature of a binary relation ≪ which is defined for normal operators A and B by: A ≪ B if there exists an operator T such that E A ( Δ ) T * E B ( Δ ) T for all Borel subset Δ of the complex plane ℂ, where E A and E B are spectral measures of A and B, respectively (the operators A and B are allowed to act in different complex Hilbert spaces). It is proved that if A ≪ B and B ≪ A, then A and B are unitarily equivalent, which shows that the relation ≪ is a partial order...

On a decomposition for pairs of commuting contractions

Zbigniew Burdak (2007)

Studia Mathematica

A new decomposition of a pair of commuting, but not necessarily doubly commuting contractions is proposed. In the case of power partial isometries a more detailed decomposition is given.

On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

Zagorodniuk, S. (1998)

Serdica Mathematical Journal

∗ Partially supported by Grant MM-428/94 of MESC.Systems of orthogonal polynomials on the real line play an important role in the theory of special functions [1]. They find applications in numerous problems of mathematical physics and classical analysis. It is known, that classical polynomials have a number of properties, which uniquely define them.

On a fixed-point theorem of Cellina

Stephen Simons (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa nota mostriamo come un teorema di esistenza per funzionali lineari porti un nuovo teorema di punto fisso che generalizza un teorema di punto fisso di Cellina.

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