Publications (Günther Hörmann)

[47] Modeling Schrödinger equation diffraction with generalized function potentials and initial values,
with Lj. Oparnica and Ch. Spreitzer
https://doi.org/10.48550/arXiv.2212.08497, Preprint at arxiv: arXiv:2212.08497 [math-ph]

[46] Dirac and normal states on Weyl-von Neumann algebras,
Lett. Math. Phys. 111, 26 (2021), https://doi.org/10.1007/s11005-021-01367-4, Preprint at arxiv: arXiv:2011.04239 [math-ph]

[45] Solution concepts, well-posedness, and wave breaking for the Fornberg-Whitham equation,
Monatsh. Math. 195(3), 421-449 (2021), https://doi.org/10.1007/s00605-020-01504-6, Preprint at arxiv: arXiv:2010.03257 [math.AP]

[44] Green Operators in Low Regularity Spacetimes and Quantum Field Theory,
with Y. Sanchez Sanchez, Ch. Spreitzer, J. Vickers
Class. Quantum Grav. 37, 175009 (2020), https://doi.org/10.1088/1361-6382/ab839a, 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
Lecture Notes in Mathematical Geophysics, available 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]

[35.5] The mathematical side of causality,
Session Notes, unpublished review of a session at the Time Machine Factory in Torino 2015

[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.