Browsing Naturwissenschaften, Mathematik und Informatik by Referee "Bahns, Dorothea Prof. Dr."
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Weakly Regular Hyperbolic Boundary Value Problems of Real Type
(20230911)In this thesis, we derive energy estimates for weakly regular hyperbolic boundary value problems of real type, for which the Lopatinskii condition degenerates in a specific way in the socalled hyperbolic region. Such ... 
Propagation of polarization sets for systems of generalized transverse type and for systems of MHD type
(20230616)Polarization sets were introduced by Dencker (1982) as a refinement of wavefront sets to the vectorvalued case. He also clarified the propagation of polarization sets when the characteristic variety of the pseudodifferential ... 
Surface waves as Fourier integral operators with complex phase
(20230616)This thesis studies linear hyperbolic boundary value problems that admit surface waves as solutions. Surface waves are related to a specific type of weakly regular hyperbolic boundary value problems, where the precise ... 
Constructive aspects of stringlocalized quantum field theory
(20220503)Stringlocalized quantum field theory (SLFT) as an alternative to gauge theory has been under investigation for the last decade because of its conceptual benefits. This thesis is dedicated to the development and investigation ... 
Harmonic analysis on 2step stratified Lie groups without the MooreWolf condition
(20220407)In this thesis we investigate harmonic analysis on a particular class of subRiemannian manifold, namely the 2step stratified Lie groups $\mathbb{G}$, as well as its applications in partial differential equations. This ... 
Structure Analysis of the PohlmeyerRehren Lie Algebra and Adaptations of the Hall Algorithm to NonFree Graded Lie Algebras
(20210614)The PohlmeyerRehren Lie algebra $\mathfrak{g}$ is an infinitedimensional $\mathbb{Z}$graded Lie algebra that was discovered in the context of string quantization in $d$dimensional spacetime by K. Pohlmeyer and his ... 
Continuous Wavelet Transformation on Homogeneous Spaces
(20210329)The classical Continuous Wavelet Transformation (cCWT) is an important and wellstudied tool in signal processing and data analysis. Because of its deep connection to representation theory, it has come into focus of pure ... 
L²Invariants for SelfSimilar CWComplexes
(20201111)L²invariants are commonly defined only for periodic spaces, that is, spaces with a cocompact action by some discrete group. This thesis develops a theory of L²invariants for quasiperiodic spaces instead, where the group ... 
Paradifferential Operators and Conormal Distributions
(20200224)In this thesis we develop a generalization of Hörmander’s symbol calculus of conor mal distributions [Hö07, Chapter 18.2] and provide techniques for applications to nonlinear hyperbolic Partial Differential Equations. ... 
Shape space in terms of Wasserstein geometry and application to quantum physics
(20181126)This thesis offers a mathematical framework to treat quantum dynamics without reference to a background structure, but rather by means of the change of the shape of the state. For this, Wasserstein geometry is used. The ... 
On the Cauchy problem for a class of degenerate hyperbolic equations
(20180831)In this thesis, a pseudodifferential calculus for a degenerate hyperbolic Cauchy problem is developed. The model for this problem originates from a certain observation in fluid mechanics, and is then extended to a more ... 
New topological and index theoretical methods to study the geometry of manifolds
(20180731)For a $\mathit{Spin}$ manifold $M$ the Rosenberg index $\alpha([M])$ is an obstruction against positive scalar curvature metrics. When $M$ is non$\mathit{Spin}$ but $\mathit{Spin}^c$, Bolotov and Dranishnikov suggested ... 
Radiative Corrections in Curved Spacetime and Physical Implications to the Power Spectrum and Trispectrum for different Inflationary Models
(20180626)In a quantum field theory with a timedependent background, as in an expanding universe, the timetranslational symmetry is broken. We therefore expect loop corrections to cosmological observables to be timedependent after ... 
Local invariants of fourdimensional Riemannian manifolds and their application to the Ricci flow
(20171215)In this thesis, we study the fourdimensional Ricci flow with the help of local invariants.If $(M^4, g(t))$ is a solution to the Ricci flow and $x \in M$, we can associate to the point $x$ a oneparameter family of curves, ... 
Scattering Resonances for Polyhedral Obstacles
(20170829)This thesis deals with the generalization of two dimensional obstacle scattering theory to polygonally bounded obstacles. Our main objective is to derive an upper bound for the counting function of the scattering poles. The ... 
Critical exponents for semilinear Tricomitype equations
(20161124)In this thesis, we consider the semilinear Tricomitype equations. In particular, we work on the global Cauchy problem for the semilinear Tricomitype equation with suitable initial data. The main objective of this thesis ... 
Braided Actions of DHR Categories and Reconstruction of Chiral Conformal Field Theories
(20161018)Quantum Field Theory (QFT) is our modern understanding of particles and matter at small scales, where quantum behaviour replaces macroscopical phenomena, which are much closer to intuition, and dynamics is rather driven ... 
Variational Estimators in Statistical Multiscale Analysis
(20160524)In recent years, a novel type of multiscale variational statistical approaches, based on socalled multiscale statistics, have received increasing popularity in various applications, such as signal recovery, imaging and ... 
Analytic singularities near radial points
(20150311)In this thesis, we applied tools of algebraic analysis and knowledge of symplectic geometry and contact geometry to give a normal form of certain class of microdifferential operators, and then studied analytic singularities of ... 
Microlocal Analysis of Tempered Distributions
(20140917)In this dissertation we study tempered distributions from the microlocal point of view. The fundamental notion of microlocal analysis, the wave front set, is replaced by two analogues, the SGwave front set and the Gwave ...