Publications (Günther Hörmann)



[43] Weak periodic solutions and numerical case studies of the Fornberg-Whitham equation,
with H. Okamoto
submitted, 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
accepted for publication, to appear in the Birkhäuser series "Trends in Mathematics, Research Perspectives", Proceedings of the ISAAC 2017 in Växjö, 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), doi: 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
accepted for publication in Math. Mech. Solids 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, 217225 (2017), Preprint at arxiv: arXiv:1512.06589 [math-ph]

[35] Conical spacetimes and global hyperbolicity,
Novi Sad Jour. Math. 45 (No. 1), 215-229 (2015), 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, 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), 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), 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.