Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Referee "Witt, Ingo Prof. Dr."
Now showing items 1-18 of 18
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Microlocal methods in quantum field theory
(2024-11-14)The renormalisation of Feynman diagrams is considered in the context of perturbative algebraic quantum field theory. The construction of Wick polynomials is related to the renormalisation of diagrams with short loops ... -
Weakly Regular Hyperbolic Boundary Value Problems of Real Type
(2023-09-11)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 so-called hyperbolic region. Such ... -
Surface waves as Fourier integral operators with complex phase
(2023-06-16)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 ... -
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 ... -
Benjamini-Schramm Convergence of Normalized Characteristic Numbers of Riemannian Manifolds
(2020-04-30)We study a weak form of Gromov-Hausdorff convergence of Riemannian manifolds, also known as Benjamini-Schramm convergence. This concept is also applicable to other areas and has widely been studied in the context of ... -
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. ... -
Coarse Cohomology with twisted Coefficients
(2019-04-18)This thesis studies sheaf cohomology on coarse spaces. -
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 ... -
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 ... -
Radiation conditions for periodic potentials
(2017-09-19)The aim of the present thesis is to determine radiation conditions for higher-dimensional Schroedinger equations with periodic potentials. There is well-known result for Helmholtz equations. However to my knowledge, there ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
The analysis of Toeplitz operators, commutative Toeplitz algebras and applications to heat kernel constructions.
(2012-06-21)This dissertation is devoted to the study of certain analytic problems inspired by recent results in the theory of Toeplitz operators on the Bergman spaces. We attack the problem of commuting Toeplitz operators with ... -
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 ...