Publications (Günther Hörmann)

[33] Elastic-gravitational equations in global seismology -- low regularity of coefficients and well-posedness,
with K. Brazda and M. V. de Hoop
in preparation

[32] Generalized functions and symplectic geometry,
with M. Kunzinger and S. Konjik
in preparation

[31] Wave equations and symmetric first-order systems in the case of low regularity,
with C. Hanel, Ch. Spreitzer, and R. Steinbauer
submitted, Preprint at arxiv: arXiv:1107.5967v2 [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
submitted, 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
to appear 2012, Preprint at arxiv: arXiv:1107.0014 [math.AP]

[27] Geometric regularization on Riemannian and Lorentzian manifolds,
with S. Dave and M. Kunzinger
to appear 2012, 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
submitted, Preprint at arxiv: arXiv:1102.2148 [math.AP]

[25] Optimal regularization processes on complete Riemannian manifolds,
with S. Dave and M. Kunzinger
submitted, 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)

Günther Hörmann