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Scientific Publications

Monographs

[M2] Geometric Theory of Generalized Functions (with Applications to General Relativity)
(This item received a Featured Review by the AMS)
Authors: Michael Grosser, Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer
MSC-class: 46F30; 35A30, 35Q75, 46-02, 46T30, 58-02, 83C99
Ref: Mathematics and its Applications, Vol. 537, Kluwer, Dodrecht, 2001.

[M1] On the foundations of nonlinear generalized functions I,II
(This item received a Featured Review by the AMS)
Authors: Eva Farkas, Michael Grosser, Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 26E15, 46E50, 35D05
Ref: Mem. Amer. Math. Soc. 729, 153, 2001.
ArXive: math.FA/9912214

Textbook

[T1] Einführung in das mathematische Arbeiten (German; Introduction into Mathematical Methodology)
Authors: Hermann Schichl, Roland Steinbauer
MSC-Class: 00A35; 00A05, 00-01
Ref: Springer, Heidelberg, 2009.

Peer-reviewed Articles

[J23] A global theory of algebras of generalized functions II: tensor distributions
Authors: Michael Grosser, Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 58J45; 35L05, 35L15, 35D99, 46F30
Ref: New York J. Math. 18, 139--199, (2012).
ArXive: arXiv:0902.1865

[J22] A geometric approach to full Colombeau algebras
Authors: Roland Steinbauer
MSC-class: 46T30; 46F30
Ref: Banach Center Publ. 88, 267--27,2 (2010).
ArXive: arXiv:0710.2096

[J21] On the Geroch-Traschen class of metrics
Authors: Roland Steinbauer, James Vickers
MSC-class: 83C75; 46T30, 53B30, 46F10, 46F30
Ref: Class. Quantum Grav. 26, 065001, (2009).
ArXive: arXiv:0811.1376

[J20] The wave equation on singular space times
Authors: James Grant, Eberhard Mayerhofer, Roland Steinbauer
MSC-class: 83C75; 46F30, 35D05, 35Q75
Ref: Commun. Math. Phys. 285(2), 399--420, (2009).
ArXive: arXiv:0710.2007

[J19] A note on distributional semi-Riemannian geometry
Authors: Roland Steinbauer
MSC-class: 46T30, 53B30, 46F10, 46F30
Ref: Novi Sad J. Math. 38 (3), 189-199 (2008).
ArXive: arXiv:0812.0173

[J18] Sheaves of nonlinear generalized functions and manifold-valued distributions
Authors: Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 46T30; 46F30, 53B20
Ref: Trans. Amer. Math. Soc. 361, 5177-5192, (2009).
ArXive: math.FA/0609358

[J17] Generalized solutions of the Vlasov-Poisson system with singular data
Authors: Irina Kmit, Michael Kunzinger, Roland Steinbauer
MSC-class: 35A05; 46F30, 35Q72, 82C22
Ref: J. Math. Anal. Appl. 340, 575-587, (2008).
ArXive: math.AP/0601552

[J16] The use of generalized functions and distributions in general relativity
(Featured as one of the highligths 2005/06 in Classical and Quantum Gravity)
Authors: Roland Steinbauer, James Vickers
MSC-class: 8302
Ref: Class. Quantum Grav. 23(10), R91-R114, (2006).
ArXive: gr-qc/0603078

[J15] Global Gronwall estimates for integral curves on Riemannian manifolds
Authors: Michael Kunzinger, Hermann Schichl, Roland Steinbauer, James Vickers
MSC-class: 53B21, 53C22, 34A26
Ref: Rev. Mat. Complut., 19(1), 133-137, (2006).
ArXive: math.DG/0412045

[J14] On classical solutions of the relativistic Vlasov-Klein-Gordon system
Authors: Michael Kunzinger, Gerhard Rein, Roland Steinbauer, Gerald Teschl
MSC-class: 35A07; 35Q72; 35Q40; 82C22
Ref: EJDE, Vol. 2005(1), 1-17, (2005).
ArXive: math.AP/0407028

[J13] Generalised connections and curvature
Authors: Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 53C05, 53B05, 46T30,46F30, 46F20
Ref: Math. Proc. Cambridge Philos. Soc. 139(3), 497--521, (2005).
ArXive: math.FA/0403040

[J12] Generalized flows and singular ODEs on differentiable manifolds
Authors: Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer, James Vickers
MSC-class: 46F30, 34G20, 46T30, 53B20
Ref: Acta Appl. Math, 80, 221-241, (2004).
ArXive: math.FA/0304131

[J11] Geodesics in spacetimes with expanding impulsive gravitational waves
Authors: Jiri Podolsky, Roland Steinbauer
MSC-class: 83C15, 83C35
PACS-class: 04.20.Jb, 04.30.Nk
Ref: Phys. Rev. D, 67, 0604013, (2003).
ArXive: gr-qc/0210007

[J10] Global weak solutions of the relativistic Vlasov-Klein-Gordon system
Authors: Michael Kunzinger, Gerhard Rein, Roland Steinbauer, Gerald Teschl
MSC-class: 35D05, 35Q72, 35Q40, 82C22
Ref: Commun. Math. Phys., 238, 367-378 (2003).
ArXive: math.AP/0209303

[J9] Intrinsic characterization of manifold-valued generalized functions
Authors: Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 46T30, 46F30, 53B20
Ref: Proc. London Math. Soc., 87(2), 451-470 (2003).
ArXive: math.FA/0107057

[J8] Generalized pseudo-Riemannian geometry
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 46T30, 46F10, 83C05
Ref: Trans. Amer. Math. Soc. 354(10), 4179-4199 (2002).
ArXive: math.FA/0107057

[J7] Remarks on the distributional Schwarzschild geometry
Authors: Mark J. Heinzle, Roland Steinbauer
MSC-class: 83C15, 83C15, 83C75, 46F30
Ref: J. Math. Phys. 43(3), 1493-1508 (2002).
ArXive: gr-qc/0112047

[J6] Foundations of a nonlinear distributional geometry
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 46T30, 46F10, 37J05
Ref: Acta Appl. Math. 71, 179-206, (2002).
ArXive: math.FA/0102019

[J5] A global theory of algebras of generalized functions
Authors: Michael Grosser, Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 46F30, 46T30
Ref: Adv. Math., 166, 50-72 (2002).
ArXive: math.FA/9912216

[J4] A note on the Penrose junction conditions
(Featured as one of the highligths 1999/2000 in Classical and Quantum Gravity)
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: Class. Quant. Grav, 16, 1255-1264 (1999).
ArXive: gr-qc/9811007

[J3] A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: J. Math. Phys, 40, 1479-1489 (1999).
ArXive: gr-qc/9806009

[J2] Geodesics and geodesic deviation for impulsive gravitational waves
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: J. Math. Phys. 39, 2201-2212 (1998).
ArXive: gr-qc/9710119

[J1] The ultrarelativistic Reissner-Nordstrom field in the Colombeau algebra
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: J. Math. Phys. 38, 1614-1622 (1997).
ArXive: gr-qc/9606059

Contributions to Proceedings

[P8] Diffeomorphism invariant Colombeau algebras. Part I: Local theory
Authors: Roland Steinbauer
MSC-class: 46F30, 46E50, 35D05, 26E15
Ref: Nonlinear Algebraic Analysis and Applications, Proceedings of the International Conference on Generalized Functions (ICGF 2000), edited by A. Delcroix, M. Hasler, J.-A. Marti and V. Valmorin, Cottenham, Cambridge, Cambridge Scientific Publishers 2004, 333-344 (2004).
ArXive: math.FA/0104269

[P7] Nonlinear distributional geometry and general relativity
Authors: Roland Steinbauer
MSC-class: 46F30, 46T30, 46F10, 83C05, 83C35
Ref: Nonlinear Algebraic Analysis and Applications, Proceedings of the International Conference on Generalized Functions (ICGF 2000), edited by A. Delcroix, M. Hasler, J.-A. Marti and V. Valmorin, Cottenham, Cambridge, Cambridge Scientific Publishers 2004, 345-356 (2004).
ArXive: math-ph/0104041

[P6] Diffeomorphism invariant construction of nonlinear generalized functions
Authors: Michael Grosser, Michael Kunzinger, Roland Steinbauer, Helmuth Urbantke, James Vickers
MSC-class: 46F30, 46T30
Ref: Proceedings of Journees Relativistes 99, Annalen der Physik, Vol 9, Spec. Iss., 173-174 (2000).
Download: here

[P5] On the impulsive limit of gravitational waves
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35
Ref: Proceedings of the Spanish Relativity Meeting. ERE-99, 307-311 (2000).
Download: here

[P4] Large space interferometer for cosmology
Authors: Karsten Danzmann S. Husa, A. Nairz, B. Pocza, R. Steinbauer
MSC-class: 83C35, 83-05, 83F05
Ref: Proposal to the European Space Agency for a Flexi Mission in Fundamental Physics, (2000).
Download: here

[P3] On the geometry of impulsive gravitational waves
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: Proceedings of the 8-th Romanian Conference on GRG (Bistrita, 1998).
ArXive: gr-qc/9809054

[P2] Distributional description of impulsive gravitational waves
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: in Nonlinear Theory of Generalized Functions, edited by Michael Grosser, Günther Hörmann, Michael Kunzinger, Michael Obergugenberger, (CRC Research Notes, 401, Boca Raton, 1999).
Download: here

[P1] ELFI, A Gravitational Wave Detector for Cosmology
Authors: S. Husa, A. Nairz, B. Pocza, R. Steinbauer
MSC-class: 83C35, 83-05, 83F05
Ref: Fundamental Physics in Space, Proceedings of the Alpbach Summer School 1997, edited by A. Wilson, 45-47 (ESA Publications Division, Noordwijk, 1997).
Download: here

Preprints

[Pre2] Wave equations and symmetric first-order systems in case of low regularity
Authors: Clemens Hanel, Günther Hörmann, Christan Spreitzer, Roland Steinbauer
MSC-class: 46F30; 35L45, 35D30, 35Q75
Status: submitted
ArXive: arXiv:1107.0014

[Pre1] Wave equations on non-smooth space-times
Authors: Günther Hörmann, Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30; 46T30, 26E15, 58B10, 46A17
Status: accepted
ArXive: arXiv:1107.0014

Miscellaneous

[EMA] Einführung in das mathematische Arbeiten: Ein Projekt zur Gestaltung der Studieneingangsphase an der Universität Wien (German; Introduction into mathematical methodology: A new strategy for the first semester)
Authors: Hermann Schichl, Roland Steinbauer
Ref: Mitteilungen der DMV (Notices of the German Mathematical Society), 17(4), 244--246, (2009).
Download: here

[H] Nonlinear Distributional Geometry
Authors: Roland Steinbauer
MSC-class: 46F30, 83C35, 83C15, 46F10, 46F05, 83C75
Ref: Habilitationsschrift at the University of Vienna, 2002.
Download: here

[Ph.D.] Distributional Methods in General Relativity
Authors: Roland Steinbauer
MSC-class: 46F30, 83C35, 83C15, 46F10, 46F05, 83C75
Ref: Ph.D. thesis at the University of Vienna, 2000.
Download: here

[M.Sc.] Colombeau Theorie und ultrarelativistischer Limes
Authors: R. Steinbauer
MSC-class: 46F30, 83C35, 83C15, 46F10, 46F05, 83C75
PACS-class: 04.20.Cv, 02.30.Sa, 04.20.Jb, 04.30.-w
Ref: Master's thesis at the University of Vienna, 1995.
Download: here

Editorial Activities

[E1] Special Issue of Integral Transforms and Special Functions
The International Conference on Generalized Functions GF 2009
Editors: Michael Grosser, Michael Kunzinger, Stevan Pilipovic, Roland Steinbauer
Ref: Taylor&Francis, 2011.

Publications listed at arXiv, MathSciNet and ZMAT

You can have a look at my preprints and publications listed at arXiv.org.

If you have permission to do so (i.e., if your home organisation is subscribed) you can also have a look at my publications

• as listed by MathSciNet, or
• as listed by Zentralblatt.