5 citations · 8 across the 12 of their papers we have counts for
13 papers
Modeling Schrödinger equation diffraction with generalized function potentials and initial values
Günther Hörmann, Ljubica Oparnica, Christian Spreitzer
We discuss spectral properties of a regularization approach to a Schrödinger equation set-up for the diffraction of a quantum particle at almost planar patterns. Physically meaning…
Generalized solutions and distributional shadows for Dirac equations
Guenther Hoermann, Christian Spreitzer
We discuss the application of recent results on generalized solutions to the Cauchy problem for hyperbolic systems to Dirac equations with external fields. In further analysis we f…
Solvability and microlocal analysis of the fractional Eringen wave equation
Günther Hörmann, Ljubica Oparnica, Dušan Zorica
We discuss unique existence and microlocal regularity properties of Sobolev space solutions to the fractional Eringen wave equation, initially given in the form of a system of equa…
Limits of regularizations for generalized function solutions to the Schrödinger equation with "square root of delta" initial value
Guenther Hoermann
We briefly review results on Colombeau type generalized solutions to the Cauchy problem for linear Schrödinger-type equations with non-smooth principal part and their compatibility…
Microlocal analysis of fractional wave equations
Günther Hörmann, Ljubica Oparnica, Dušan Zorica
We determine the wave front sets of solutions to two special cases of the Cauchy problem for the space-time fractional Zener wave equation, one being fractional in space, the other…
A regularization approach to non-smooth symplectic geometry
Guenther Hoermann, Sanja Konjik, Michael Kunzinger
We introduce non-smooth symplectic forms on manifolds and describe corresponding Poisson structures on the algebra of Colombeau generalized functions. This is achieved by establish…
Symplectic modules over Colombeau-generalized numbers
Sanja Konjik, Guenther Hoermann, Michael Kunzinger
We study symplectic linear algebra over the ring $\Rt$ of Colombeau generalized numbers. Due to the algebraic properties of $\Rt$ it is possible to preserve a number of central res…
The wave equation with a discontinuous coefficient depending on time only: generalized solutions and propagation of singularities
Hideo Deguchi, Guenther Hoermann, Michael Oberguggenberger
This paper is devoted to the investigation of propagation of singularities in hyperbolic equations with non-smooth oefficients, using the Colombeau theory of generalized functions.…
Wave equations and symmetric first-order systems in case of low regularity
Clemens Hanel, Günther Hörmann, Christian Spreitzer +1
We analyse an algorithm of transition between Cauchy problems for second-order wave equations and first-order symmetric hyperbolic systems in case the coefficients as well as the d…
Symmetric hyperbolic systems in algebras of generalized functions and distributional limits
Guenther Hoermann, Christian Spreitzer
We study existence, uniqueness, and distributional aspects of generalized solutions to the Cauchy problem for first-order symmetric (or Hermitian) hyperbolic systems of partial dif…
Wave equations on non-smooth space-times
Guenther Hoermann, Michael Kunzinger, Roland Steinbauer
We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem…
Geometric regularization on Riemannian and Lorentzian manifolds
Shantanu Dave, Guenther Hoermann, Michael Kunzinger
We investigate regularizations of distributional sections of vector bundles by means of nets of smooth sections that preserve the main regularity properties of the original distrib…
Optimal regularization processes on complete Riemannian manifolds
Shantanu Dave, Guenther Hoermann, Michael Kunzinger
We study regularizations of Schwartz distributions on a complete Riemannian manifold . These approximations are based on families of smoothing operators obtained from the soluti…