Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Referee "Bahns, Dorothea Prof. Dr."
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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 ... 
C*quantum groups with projection
(20140625)We propose a general theory to study semidirect products of C quantum groups in the framework of multiplicative unitaries. Starting from a quantum group with a projection we decompose its multiplicative unitary as a product ... 
Composition theorems for paired Lagrangian distributions
(20120412)The aim of this research is to determine whether the composition of paired Lagrangian distributions belongs to wellknown classes such as marked Lagrangian, isotropic Lagrangian, paired Lagrangian or generalized ... 
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 ... 
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 ... 
Existence of solutions of quasilinear elliptic equations on manifolds with conic points
(20140515)Existence and regularity of solutions of quasilinear elliptic equations in nonsmooth domains have been interesting topics in the development of partial differential equations. The existence of finiteenergy solutions of ... 
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 ... 
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, ... 
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 ... 
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 ... 
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 ... 
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 ... 
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. ... 
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 ... 
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 ... 
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 ... 
Singularities of twopoint functions in Quantum Field Theory
(20130828)The main topic of the present thesis is the study of singularities of twopoint functions of spin0 and spin1/2 quantum fields, possibly set on curved spacetime or in the presence of smooth, external electromagnetic ... 
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 ... 
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 ... 
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 ...