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Linear Operators (linear + operators)

Distribution by Scientific Domains

Information Science and Computing	50%
Mathematics and Statistics	33%

Selected Abstracts

Remarks on Duality in Graph Spaces of First-Order Linear Operators

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006
Max JensenArticle first published online: 4 DEC 200
Graph spaces provide a setting alternative to Sobolev spaces and BV spaces, which is suitable for the analysis of first-order linear boundary value problems such as Friedrichs systems. Besides investigations of the well-posedness of the continuous problem there is also an increasing interest in the error analysis of finite element methods within a graph space framework. In this text we elucidate various methods for an explicit representation of dual spaces of graph spaces. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Differential Representations for Mesh Processing

COMPUTER GRAPHICS FORUM, Issue 4 2006
Olga Sorkine
Abstract Surface representation and processing is one of the key topics in computer graphics and geometric modeling, since it greatly affects the range of possible applications. In this paper we will present recent advances in geometry processing that are related to the Laplacian processing framework and differential representations. This framework is based on linear operators defined on polygonal meshes, and furnishes a variety of processing applications, such as shape approximation and compact representation, mesh editing, watermarking and morphing. The core of the framework is the definition of differential coordinates and new bases for efficient mesh geometry representation, based on the mesh Laplacian operator. [source]

Kinks and rotations in long Josephson junctions

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2001
Wolfgang Hauck
Abstract Kinks and rotations are studied in long Josephson junctions for small and large surface losses. Geometric singular perturbation theory is used to prove existence for small surface losses, while numerical continuation is necessary to handle large surface losses. A survey of the system behaviour in terms of dissipation parameters and bias current is given. Linear orbital stability for kinks is proved for small surface losses by calculating the spectrum of the linearized problem. The spectrum is split into essential spectrum and discrete spectrum. For the determination of the discrete spectrum, robustness of exponential dichotomies is used. Puiseux series together with perturbation theory for linear operators are an essential tool. In a final step, a smooth Evans function together with geometric singular perturbation theory is used to count eigenvalues. For kinks, non-linear orbital stability is shown. For this purpose, the asymptotic behaviour of a semigroup is given and the theory of centre and stable manifolds is applied. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Evolution operators generated by non-densely defined operators

MATHEMATISCHE NACHRICHTEN, Issue 11 2005
Hirokazu Oka
Abstract In this paper it is shown that an evolution operator is generated by a family of closed linear operators whose common domain is not necessarily dense in the underlying Banach space, under the stability condition proposed by the second author from the viewpoint of finite difference approximations. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Computability of compact operators on computable Banach spaces with bases

MLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 4-5 2007
Vasco Brattka
Abstract We develop some parts of the theory of compact operators from the point of view of computable analysis. While computable compact operators on Hilbert spaces are easy to understand, it turns out that these operators on Banach spaces are harder to handle. Classically, the theory of compact operators on Banach spaces is developed with the help of the non-constructive tool of sequential compactness. We demonstrate that a substantial amount of this theory can be developed computably on Banach spaces with computable Schauder bases that are well-behaved. The conditions imposed on the bases are such that they generalize the Hilbert space case. In particular, we prove that the space of compact operators on Banach spaces with monotone, computably shrinking, and computable bases is a computable Banach space itself and operations such as composition with bounded linear operators from left are computable. Moreover, we provide a computable version of the Theorem of Schauder on adjoints in this framework and we discuss a non-uniform result on composition with bounded linear operators from right. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

F-products and nonstandard hulls for semigroups

MLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 1 2004
Jakob Kellner
Abstract Derndinger [2] and Krupa [5] defined the F-product of a (strongly continuous one-parameter) semigroup (of linear operators) and presented some applications (e. g. to spectral theory of positive operators, cf. [3]). Wolff (in [7] and [8]) investigated some kind of nonstandard analogon and applied it to spectral theory of group representations. The question arises in which way these constructions are related. In this paper we show that the classical and the nonstandard F-product are isomorphic (Theorem 2.6). We also prove a little "classical" corollary (2.7.). (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]