Now showing items 1-18 of 18

• #### Analytic singularities near radial points ﻿

(2015-03-11)
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 ﻿

(2014-06-25)
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 ﻿

(2012-04-12)
The aim of this research is to determine whether the composition of paired Lagrangian distributions belongs to well-known classes such as marked Lagrangian, isotropic Lagrangian, paired Lagrangian or generalized ...
• #### Continuous Wavelet Transformation on Homogeneous Spaces ﻿

(2021-03-29)
The classical Continuous Wavelet Transformation (cCWT) is an important and well-studied 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 Tricomi-type equations ﻿

(2016-11-24)
In this thesis, we consider the semilinear Tricomi-type equations. In particular, we work on the global Cauchy problem for the semilinear Tricomi-type equation with suitable initial data. The main objective of this thesis ...
• #### Existence of solutions of quasilinear elliptic equations on manifolds with conic points ﻿

(2014-05-15)
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 finite-energy solutions of ...
• #### Harmonic analysis on 2-step stratified Lie groups without the Moore-Wolf condition ﻿

(2022-04-07)
In this thesis we investigate harmonic analysis on a particular class of sub-Riemannian manifold, namely the 2-step stratified Lie groups $\mathbb{G}$, as well as its applications in partial differential equations. This ...
• #### Local invariants of four-dimensional Riemannian manifolds and their application to the Ricci flow ﻿

(2017-12-15)
In this thesis, we study the four-dimensional 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 one-parameter family of curves, ...
• #### L²-Invariants for Self-Similar CW-Complexes ﻿

(2020-11-11)
L²-invariants are commonly defined only for periodic spaces, that is, spaces with a cocompact action by some discrete group. This thesis develops a theory of L²-invariants for quasi-periodic spaces instead, where the group ...
• #### Microlocal Analysis of Tempered Distributions ﻿

(2014-09-17)
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 SG-wave front set and the G-wave ...
• #### New topological and index theoretical methods to study the geometry of manifolds ﻿

(2018-07-31)
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 ﻿

(2018-08-31)
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 ﻿

(2020-02-24)
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. ...
• #### Scattering Resonances for Polyhedral Obstacles ﻿

(2017-08-29)
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 ﻿

(2018-11-26)
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 two-point functions in Quantum Field Theory ﻿

(2013-08-28)
The main topic of the present thesis is the study of singularities of two-point functions of spin-0 and spin-1/2 quantum fields, possibly set on curved spacetime or in the presence of smooth, external electromagnetic ...
• #### Structure Analysis of the Pohlmeyer-Rehren Lie Algebra and Adaptations of the Hall Algorithm to Non-Free Graded Lie Algebras ﻿

(2021-06-14)
The Pohlmeyer-Rehren Lie algebra $\mathfrak{g}$ is an infinite-dimensional $\mathbb{Z}$-graded Lie algebra that was discovered in the context of string quantization in $d$-dimensional spacetime by K. Pohlmeyer and his ...
• #### Variational Estimators in Statistical Multiscale Analysis ﻿

(2016-05-24)
In recent years, a novel type of multiscale variational statistical approaches, based on so-called multiscale statistics, have received increasing popularity in various applications, such as signal recovery, imaging and ...