Stuttgart, Univ., Diplomarb., 2000.

Zugl.: Hannover, Univ., Diss., 2008

Zugl.: Dresden, Techn. Univ., Diss., 2005

Zugl.: Braunschweig, Techn. University, Diss., 2003.

Univ., Diss.--Tübingen, 1998. / A rev. version of the author's dissertation (doctoral--Tübingen). Includes bibliographical references. Literaturverz. S. [163] - 170.

Eine klassische Art, die Dynamik nichtlinearer Systeme zu beschreiben, besteht in der Analyse ihrer Fourierspektren. Für periodische und quasiperiodische Prozesse besteht das Fourierspektrum nur aus diskreten Deltafunktionen. Das Spektrum einer chaotischen Bewegung ist hingegen durch das Vorhandensein einer stetigen Komponente gekennzeichnet. In der Arbeit geht es um einen eigenartigen, weder regulären noch vollständig chaotischen Zustand mit sogenanntem singulärstetigen Leistungsspektrum. <br /> Unsere Analyse ergab verschiedene Fälle aus weit auseinanderliegenden Gebieten, in denen singulär stetige (fraktale) Spektren auftreten. Die Beispiele betreffen sowohl physikalische Prozesse, die auf iterierte diskrete Abbildungen oder gar symbolische Sequenzen reduzierbar sind, wie auch Prozesse, deren Beschreibung auf den gewöhnlichen oder partiellen Differentialgleichungen basiert. / One of the classical ways to describe the dynamics of nonlinear systems is to analyze theur Fourier spectra. For periodic and quasiperiodic processes the Fourier spectrum consists purely of discrete delta-functions. On the contrary, the spectrum of a chaotic motion is marked by the presence of the continuous component. In this work, we describe the peculiar, neither regular nor completely chaotic state with so called singular-continuous power spectrum. <br /> Our investigations concern various cases from most different fields, where one meets the singular continuous (fractal) spectra. The examples include both the physical processes which can be reduced to iterated discrete mappings or even symbolic sequences, and the processes whose description is based on the ordinary or partial differential equations.

Zugl.: Aachen, Techn. Hochsch., Diss., 2006.

In this work the methods of mode decomposition and Fourier analysis of quantum fields on curved spacetimes previously available mainly for the scalar fields on Friedman-Robertson-Walker spacetimes are extended to arbitrary vector fields on general spatially homogeneous spacetimes. This is done by developing a rigorous unified framework which incorporates mode decomposition, harmonic analysis and Fourier analysis. Explicit constructions are performed for a variety of situations arising in homogeneous cosmology. A number of results concerning classical and quantum fields known for very restricted situations are generalized to cover almost all cosmological models.

No description available.

Within the past decades, wavelets and associated wavelet transforms have been intensively investigated in both applied and pure mathematics. They and the related multi-scale analysis provide essential tools to describe, analyse and modify signals, images or, in rather abstract concepts, functions, function spaces and associated operators. We introduce the concept of diffusive wavelets where the dilation operator is provided by an evolution like process that comes from an approximate identity. The translation operator is naturally defined by a regular representation of the Lie group where we want to construct wavelets. For compact Lie groups the theory can be formulated in a very elegant way and also for homogeneous spaces of those groups we formulate the theory in the theory of non-commutative harmonic analysis. Explicit realisation are given for the Rotation group SO(3), the k-Torus, the Spin group and the n-sphere as homogeneous space. As non compact example we discuss diffusive wavelets on the Heisenberg group, where the construction succeeds thanks to existence of the Plancherel measure for this group. The last chapter is devoted to the Radon transform on SO(3), where the application on diffusive wavelets can be used for its inversion. The discussion of a variational spline approach provides criteria for the choice of points for measurements in concrete applications.