# Publications (Günther Hörmann)

** [44] Green Operators in Low Regularity Spacetimes and Quantum Field Theory**,

with Y. Sanchez Sanchez, Ch. Spreitzer, J. Vickers

*Preprint at arxiv: *
arXiv:1910.13789 [gr-qc]

** [43] Weak periodic solutions and numerical case studies of the Fornberg-Whitham equation**,

with H. Okamoto

*Discr. Cont. Dyn. Syst. Ser. A 39 (8), 4455-4469 (2019)*, https://doi.org/10.3934/dcds.2019182, *Preprint at arxiv: *
arXiv:1807.02320 [math.AP]

** [42] Discontinuous traveling waves as weak solutions to the Fornberg-Whitham equation**,

*Jour. Diff. Equs. 265 (7), 2825-2841 (2018)*, https://doi.org/10.1016/j.jde.2018.04.056,
*Preprint at arxiv: *
arXiv:1802.00215 [math.AP]

** [41] Generalized solutions and distributional shadows for Dirac equations**,

with Ch. Spreitzer

in *Analysis, Probability, Applications, and Computation*, "Trends in Mathematics, Research Perspectives", Birkhäuser 2019, pp. 419-428,
https://doi.org/10.1007/978-3-030-04459-6,
*Preprint at arxiv: *
arXiv:1712.09690 [math-ph]

** [40] Wave breaking of periodic solutions to the Fornberg-Whitham equation**,

*Discr. Cont. Dyn. Syst. Ser. A, 38 (3), 1605-1613 (2018),*
https://doi.org/10.3934/dcds.2018066,
*Preprint at arxiv: *
arXiv:1707.05838 [math.AP]

** [39] Solvability and microlocal analysis of the fractional Eringen wave equation**,

with Lj. Oparnica and D. Zorica

*Math. Mech. Solids 23 (No. 10), 1420-1430 (2018)*, https://doi.org/10.1177/1081286517726371,
*Preprint at arxiv: *
arXiv:1703.01911 [math.AP]

** [38] Limits of regularizations for generalized function solutions to the
Schrödinger equation with "square root of delta" initial value**,

*J. Fourier Anal. Appl. 24(4), 1160-1179 (2018)*, https://doi.org/10.1007/s00041-017-9548-4, *Preprint at arxiv:* arXiv:1612.09055 [math.FA]

** [37] Variational formulation of the earth's elastic-gravitational
deformations under low regularity conditions**,

with K. Brazda and M. V. de Hoop

book chapter,
*Preprint at arxiv:* arXiv:1702.04741 [math-ph]

** [36] Microlocal analysis of fractional wave equations**,

with Lj. Oparnica and D. Zorica

*Z. Angew. Math. Mech. 97, 217–225 (2017)*, https://doi.org/10.1002/zamm.201600036, *Preprint at arxiv:* arXiv:1512.06589 [math-ph]

** [35] Conical spacetimes and global hyperbolicity**,

*Novi Sad Jour. Math. 45 (No. 1), 215-229 (2015)*, https://doi.org/10.30755/nsjom.gf14.02 *Preprint at arxiv:* arXiv:1501.00672 [math-ph]

** [34] A regularization approach to non-smooth symplectic geometry**,

with M. Kunzinger and S. Konjik

in *Operator Theory:
Advances and Applications, volume 245, Birkhaeuser 2015, pp.
119-132*, https://doi.org/10.1007/978-3-319-14618-8_10, *Preprint at arxiv:* arXiv:1403.0234 [math.DG]

** [33] The globally hyperbolic metric splitting for non-smooth wave-type space-times**,

with C. Sämann

*J. Math. Anal. Appl. 420, 348-363 (2014)*, https://doi.org/10.1016/j.jmaa.2014.05.086,
*Preprint at arxiv:* arXiv:1310.1310 [math-ph]

** [32] Symplectic modules over Colombeau-generalized numbers**,

with M. Kunzinger and S. Konjik

*Comm. Algebra 42, 3558-3577 (2014)*,https://doi.org/10.1080/00927872.2013.790037, *Preprint at arxiv:* arXiv:1211.2629 [math.RA]

** [31] Wave equations and symmetric first-order systems in the case of low
regularity**,

with C. Hanel, Ch. Spreitzer, and R. Steinbauer

in *Operator Theory:
Advances and Applications, volume 231, Birkhaeuser 2013, pp.
273-286*, *Preprint at arxiv:* arXiv:1202.0406 [math.AP]

** [30] The wave equation with a discontinuous coefficient depending on time only: generalized solutions and propagation of singularities**,

with H. Deguchi and M. Oberguggenberger

in *Operator Theory:
Advances and Applications, volume 231, Birkhaeuser 2013, pp.
313-329*, *Preprint at arxiv:* arXiv:1202.1134v1 [math.AP]

** [29] Symmetric hyperbolic systems in algebras of generalized functions
and distributional limits**,

with C. Spreitzer

*J. Math. Anal. Appl. 388, 1166-1179 (2012)*, *Preprint at arxiv:* arXiv:1107.5967 [math.AP]

** [28] Wave equations on non-smooth space-times**,

with M. Kunzinger and R. Steinbauer

in *Evolution Equations of Hyperbolic and
Schrödinger Type, Progress in Mathematics, volume 301, Birkhaeuser 2012, pp.
163-186 *,
*Preprint at arxiv:* arXiv:1107.0014 [math.AP]

** [27] Geometric regularization on Riemannian and Lorentzian manifolds**,

with S. Dave and M. Kunzinger

in *Evolution Equations of Hyperbolic and
Schrödinger Type, Progress in Mathematics, volume 301, Birkhaeuser 2012, pp.
87-102,*
*Preprint at arxiv:* arXiv:1107.0010 [math.FA]

** [26] Generalized solutions for the Euler-Bernoulli model with Zener viscoelastic foundations and distributional forces**,

with S. Konjik and Lj. Oparnica

*Analysis and Applications 11, (2013), 1350017*, *Preprint at arxiv:* arXiv:1102.2148 [math.AP]

** [25] Optimal regularization processes on complete Riemannian
manifolds**,

with S. Dave and M. Kunzinger

*Tokyo Jour. Math. 36, 25-47 (2013)*, *Preprint at arxiv:* arXiv:1003.3341 [math.FA]

** [24] The Cauchy problem for Schrödinger-type partial differential operators with generalized functions in the principal part and as data**,

*Monatsh. Math. 163, 445-460 (2011)*, *Preprint at arxiv:* arXiv:0909.5672 [math.FA]

** [23] Generalized solutions for the Euler-Bernoulli model with distributional forces**,

with Lj. Oparnica

*J. Math. Anal. Appl. 357, 142-153 (2009)*,
*Preprint at arxiv:* arXiv:0812.1958 [math.FA]

** [22] Comparison of some solution concepts for linear first-order hyperbolic differential equations with non-smooth coefficients**,

with Simon Haller

*Publ. de l'Inst. Math. 84 (98), 123-157 (2008)*,
*Preprint: * arXiv:0712.1669 [math.AP]

** [21] Generalized oscillatory integrals and Fourier integral operators**,

with C. Garetto and M. Oberguggenberger

*Proc. Edinb. Math. Soc. 52, 351-386 (2009)*,
*Preprint at arxiv:* math.AP/0607706

** [20] Distributional solution concepts for the Euler-Bernoulli beam equation
with discontinuous coefficients**,

with Lj. Oparnica

*Applicable Analysis 86, 1347-1363 (2007)*,
*Preprint at arxiv:* math/0606058

** [19] On duality theory and pseudodifferential techniques for Colombeau
algebras: generalized delta functionals, kernels and wave front sets**,

with C. Garetto

* Bull. Acad. Serbe Cl. Sci.,31, 115-136 (2006)*,
*Preprint*,
*arxiv:* math.FA/0507222

** [18] Fourier-integral operator approximation of solutions to
first-order hyperbolic pseudodifferential equations II:
microlocal analysis**,

with J. Le Rousseau

*Jour. Math. Pures Appliquees 86, 403-426 (2006)*,
preprint

** [17] Evolution systems for paraxial wave equations of
Schrödinger-type with non-smooth coefficients**,

with M. de Hoop and M. Oberguggenberger

*Jour. Diff. Equs. 245 (2008)*, 1413-1432,
*Preprint at arxiv:* math.AP/0506410

** [16] Microlocal analysis of generalized functions: pseudodifferential techniques
and propagation of singularities **,

with C. Garetto

*Proc. Edinb. Math. Soc. 48, 603-629 (2005)*,
*Preprint at arxiv:* math.AP/0401397

** [15] Microlocal hypoellipticity of linear partial differential operators with
generalized functions as coefficients**,

with M. Oberguggenberger and S. Pilipovic

*Trans. Amer. Math. Soc. 358, 3363-3383 (2006)*(
Abstract),
*Preprint at arxiv:* math.AP/0303248

** [14] Elliptic regularity and solvability for partial differential equations with
Colombeau coefficients**,

with M. Oberguggenberger

*Electr. Jour. Diff. Equ., Vol. 2004, 1-30 *,
*Retrieve:*
directly from EJDE

** [13] First order hyperbolic pseudodifferential equations with generalized symbols,**

*J. Math. Anal. Appl. 293, 40-56 (2004)*,
*Preprint at arxiv:* math.AP/0307406

** [12] Hölder-Zygmund regularity in algebras of generalized functions**,

*Z. Anal. Anwendungen 23, 139-165 (2004)*,
*Preprint at arxiv:* math.AP/0112222

** [11] Geophysical modeling with Colombeau functions: Microlocal properties and
Zygmund regularity**,

with M. V. de Hoop

*in 'Nonlinear Algebraic Analysis', eds. A. Delcroix, M. Hasler, J.-A. Marti,
V. Valmorin, Cambridge Scientific Publishers, Cambridge, 2004 *

*Preprint at arxiv:* math.AP/0104007

** [10] Detection of wave front set perturbations via correlation: Foundation for
wave-equation tomography**,

with M. V. de Hoop

*Appl. Anal. 81, 1443-1465 (2002)*,
*Preprint at arxiv:* math-ph/0104003

** [9] A note on representations of the finite Heisenberg group and sums of greatest
common divisors**,

with J. Grassberger

*Discrete Math. Theor. Comput. Sci. 4, 91-100 (2001)*,
*Retrieve:* directly from DMTCS

** [8] Semilinear hyperbolic systems with singular nonlocal boundary conditions:
reflection of singularities and delta-waves **,

with I. Kmit

*Z. Anal. Anwendungen 20, 637-659 (2001)*

** [7] Microlocal analysis and global solutions of some hyperbolic equations with
discontinuous coefficients**,

with M. V. de Hoop

*Acta Appl. Math. 67, 173-224 (2001)* ( Preprint version )

** [6] Microlocal properties of basic operations in Colombeau algebras**,

with M. Kunzinger

*J. Math. Anal. Appl. 261, 254-270 (2001)*,
*Preprint at arxiv:* math.FA/0008206

** [5] Regularized derivatives in a 2-dimensional model of self-interacting fields
with singular data**,

with M. Kunzinger

*Z. Anal. Anwendungen 19, 147-158 (2000)*,
*Preprint at arxiv:* math.AP/9912219

** [4] Integration and microlocal analysis in Colombeau algebras**,

*J. Math. Anal. Appl. 239, 332-348 (1999)*
( Preprint version and errata )

** [3] Nonlinearity and self-interaction in physical field theories with
singularities**,

with M. Kunzinger

*Integral Transform Spec. Funct. 6, 205-214 (1998)*

** [2] Regular Weyl-systems and smooth structures on Heisenberg groups**,

*Commun. Math. Phys. 184, 51-63 (1997)*

** [1] Galilei invariant molecular dynamics**,

with C. Jaekel

*Publ. Res. Inst. Math. Sci. 31, 805-827 (1995)*

** [0] The Weyl algebra on the two-torus**,

*NTZ/INTSEM Nr. 34 on Entropy and dynamical entropy in mathematical physics,*

August 1991, University of Leipzig,
Preprint version

** [-1] Representations of the infinite dimensional Heisenberg group**,

Dissertation, Universität Wien 1993.

** [-2] Darstellungen der Weyl-Relationen**,

Diplomarbeit, Universität Wien 1991.