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Spectral Theory (spectral + theory)

Distribution by Scientific Domains
Mathematics and Statistics87%

Selected Abstracts

Spectral Theory for Perturbed Systems

GAMM - MITTEILUNGEN, Issue 1 2009
Fritz Colonius
Abstract This paper presents an overview of topological, smooth, and control techniques for dynamical systems and their interrelations for the study of perturbed systems. We concentrate on spectral analysis via linearization of systems. Emphasis is placed on parameter dependent perturbed systems and on a comparison of the Markovian and the dynamical structure of systems with Markov diffusion perturbation process. A number of applications is provided (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Spectral theory,50 years of progress and a conclusion

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2001
D. B. Pearson
First page of article [source]

Spectral theory and iterative methods for the Maxwell system in nonsmooth domains

MATHEMATISCHE NACHRICHTEN, Issue 6 2010
Irina Mitrea
Abstract We study spectral properties of boundary integral operators which naturally arise in the study of the Maxwell system of equations in a Lipschitz domain , , ,3. By employing Rellich-type identities we show that the spectrum of the magnetic dipole boundary integral operator (composed with an appropriate projection) acting on L2(,,) lies in the exterior of a hyperbola whose shape depends only on the Lipschitz constant of ,. These spectral theory results are then used to construct generalized Neumann series solutions for boundary value problems associated with the Maxwell system and to study their rates of convergence (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Integrable operators and canonical differential systems

MATHEMATISCHE NACHRICHTEN, Issue 1-2 2007
Lev Sakhnovich
Abstract In this article we consider a class of integrable operators and investigate its connections with the following theories: the spectral theory of the non-self-adjoint operators, the Riemann-Hilbert problem, the canonical differential systems, the random matrices theory and the limit values of the multiplicative integral. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Spectral analysis of fourth order differential operators I

MATHEMATISCHE NACHRICHTEN, Issue 1-2 2006
Horst Behncke
Abstract We study the spectral theory of differential operators of the form on ,2w(0, ,). By means of asymptotic integration, estimates for the eigenfunctions andM -matrix are derived. Since the M -function is the Stieltjes transform of the spectral measure, spectral properties of , are directly related to the asymptotics of the eigenfunctions. The method of asymptotic integration, however, excludes coefficients which are too oscillatory or whose derivatives decay too slowly. Consequently there is no singular continuous spectrum in all our cases. This was found earlier for Sturm,Liouville operators, for which theWKB method provides a good approximation. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Deficiency indices and spectral theory of third order differential operators on the half line

MATHEMATISCHE NACHRICHTEN, Issue 12-13 2005
Horst Behncke
Abstract We investigate the spectral theory of a general third order formally symmetric differential expression of the form acting in the Hilbert space ,2w(a ,,). A Kummer,Liouville transformation is introduced which produces a differential operator unitarily equivalent to L . By means of the Kummer,Liouville transformation and asymptotic integration, the asymptotic solutions of L [y ] = zy are found. From the asymptotic integration, the deficiency indices are found for the minimal operator associated with L . For a class of operators with deficiency index (2, 2), it is further proved that almost all selfadjoint extensions of the minimal operator have a discrete spectrum which is necessarily unbounded below. There are however also operators with continuous spectrum. (© 2005 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]