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Michael Kunzinger - Publications

Publications


Books

[B3] Geometric Theory of Generalized Functions
with Applications to General Relativity
with M. Grosser, M. Oberguggenberger and R. Steinbauer
Mathematics and its Applications 537, Kluwer, 2001.

[B2] On the Foundations of Nonlinear Generalized Functions I, II.
with E. Farkas, M. Grosser and R. Steinbauer
Retrieve: math.FA/9912214 [abs, src, pdf, other]
and math.FA/9912215 [abs, src, pdf, other]
Mem. Amer. Math. Soc. 153, No. 729, 2001.

[B1] Barrelledness, Baire-like and (LF)-Spaces ,
Pitman Research Notes in Mathematics Vol. 298, Longman, Harlow 1993,
Review in Bull. AMS 32 (3) (1995), 354-357 .


Publications in refereed Journals

[J46] The Hawking-Penrose singularity theorem for $C^{1,1}$-Lorentzian metrics
with M. Graf, J. D. E. Grant, and R. Steinbauer
Subj-class: General Relativity and Quantum Cosmology, Differential Geometry
MSC-class: 83C75, 53B30
Retrieve: 1706.08426
Journal: Comm. Math. Phys., to appear.

[J45] Well-posedness theory for degenerate parabolic equations on Riemannian manifolds
with M. Graf and D. Mitrovic
Subj-class: Analysis of PDE
MSC-class:35K65, 42B37, 76S99
Retrieve: 1612.08195
Journal: J. Differential Equations 263, no. 8, 4787-4825 (2017).

[J44] Singular reduction modules of differential equations
with V.M. Boyko and R. Popovych
Subj-class: Mathematical Physics, Symmetry Analysis
MSC-class: 35A30, 35C05, 35K55, 35K55, 35L70
Retrieve: 1201.3223
Journal: J. Math. Phys. 57, 101503 (2016)

[J43] A convenient notion of compact set for generalized functions
with P. Giordano
Subj-class: Functional Analysis
MSC-class:46F30, 46A13, 13J99
Retrieve: 1411.7292
Journal: Proc. Edinburgh Math. Soc., to appear.

[J42] The Penrose singularity theorem in regularity $C^{1,1}$
with R. Steinbauer and J. A. Vickers
Subj-class: General Relativity and Quantum Cosmology, Differential Geometry
MSC-class: 83C75, 53B30
Retrieve: 1502.00287
Journal: Class. Quant. Grav., 32 (2015), no. 15, 155010, 12 pp.
This article was featured among the Highlights of 2014-2015 in Mathematical Relativity by the Editorial Board of Classical and Quantum Gravity.

[J41] Hawking's singularity theorem for $C^{1,1}$-metrics
with R. Steinbauer, M. Stojkovic, and J. A. Vickers
Subj-class: General Relativity and Quantum Cosmology, Differential Geometry
MSC-class: 83C75, 53B30
Retrieve: 1411.4689
Journal: Class. Quant. Grav., 32 (2015), no. 7, 075012, 19 pp.
This article was featured among the Highlights of 2014-2015 in Mathematical Relativity by the Editorial Board of Classical and Quantum Gravity.

[J40] Strongly internal sets and generalized smooth functions
with P. Giordano and H. Vernaeve
Subj-class: Functional Analysis
MSC-class:46F30, 03H05, 46S20
Retrieve: 1402.3534
Journal: J. Math. Anal. Appl., 422 (2015), no. 1, 56-71.

[J39] A regularisation approach to causality theory for $C^{1,1}$-Lorentzian metrics
with R. Steinbauer, M. Stojkovic, and J. A. Vickers
Subj-class: Differential Geometry
MSC-class:53B30
Retrieve: 1310.4404
Journal: Gen. Relativ. Gravit. (2014) 46:1738.

[J38] The exponential map of a $C^{1,1}$-metric
with R. Steinbauer and M. Stojkovic
Subj-class: Differential Geometry
MSC-class:53B20, 53B21, 53B30
Retrieve: 1306.4776
Journal: Differential Geom. Appl. 34, 14-24, 2014.

[J37] Symplectic modules over Colombeau-generalized numbers
with G. Hörmann and S. Konjik
Subj-class: Rings and Algebras, Linear Algebra
MSC-class: 15A63, 15A18, 15A21, 46F30
Retrieve: 1211.2629
Journal: Comm. Algebra 42: 3358-3577, 2014.

[J36] Singularity structures for noncommutative spaces
with S. Dave
Subj-class: Global Analysis
MSC-class: 58J40, 58J47, 58J42
Retrieve: 1111.6570
Journal: Trans. Amer. Math. Soc., 367, no. 1, 251-273, 2015.

[J35] Optimal regularization processes on complete Riemannian manifolds
with S. Dave and G. Hörmann
Subj-class: Functional Analysis, Global Analysis
MSC-class: 58J37,46F30,46T30,35A27,35L05
Retrieve: 1003.3341
Journal: Tokyo J. Math., Vol. 36, No. 1, 2013.

[J34] New topologies on Colombeau generalized numbers and the Fermat-Reyes theorem
with P. Giordano
Subj-class: Functional Analysis, Algebras of Generalized Functions
MSC-class: 46F30, 46T20
Retrieve: 1201.3887
Journal: J. Math. Anal. Appl., 399 (2013), no. 1, 229238.

[J33] A global theory of algebras of generalized functions II: tensor distributions
with M. Grosser, R. Steinbauer, and J. Vickers
Subj-class: Functional Analysis, Global Analysis
MSC-class: 46F30; 46T30, 26E15, 58B10, 46A17
Retrieve: 0902.1865
Journal: New York J. Math. 18 (2012) 139-199.

[J32] Manifold-valued generalized functions in full Colombeau spaces
with E. Nigsch
Subj-class: Functional Analysis
MSC-class: 46F30,46T30,26E15
Retrieve: 1103.5845
Journal: Comm. Math. Univ. Carolinae 52 (4) (2011) 519-534.

[J31] Topological and algebraic structures on the ring of Fermat reals
with Paolo Giordano
Subj-class: Commutative Algebra
MSC-class: 03H05, 12D, 13J25
Retrieve: 1104.1492
Journal: Israel J. Math., 193 (2013), no. 1, 459505.

[J30] Algebras of generalized functions with smooth parameter dependence
with A. Burtscher
Subj-class: Functional Analysis, Algebra
MSC-class: 46F30,13J25,46T30
Retrieve: 1010.5752
Journal: Proc. Edinburgh Math. Soc. (Series 2), Vol. 55, Issue 01, pp 105 - 124, 2012.

[J29] Generalized conditional symmetries of evolution equations
with R. Popovych
Subj-class: Mathematical Physics, Analysis of PDE
MSC-class: 35B06, 35K55, 35K57, 35C05
Retrieve: 1011.0277
Journal: J. Math. Anal. Appl. 379 No. 1, 444-460, 2011.

[J28] Singular reduction operators in two dimensions.
with R. Popovych
Subj-class: Symmetry group analysis of PDEs; Mathematical Physics
MSC-class: 35A30, 35C05, 35K55, 35K55, 35L70
Retrieve: 0808.3577
Journal: J. Phys. A: Math. Theor. 41 (2008) 505201.

[J27] Admissible transformations of nonlinear Schrödinger equations.
with R. Popovych and H. Eshragi
Subj-class: Symmetry group analysis of PDEs; Mathematical Physics
MSC-class: 35A30; 35Q55;58J70;35C05
Retrieve: math-ph/0611061 [abs, src, pdf, other]
Journal: Acta. Appl. Math. 109, 315-359 (2010).

[J26] Potential Conservation Laws.
with R. Popovych
Subj-class: Symmetry group analysis of PDEs; Mathematical Physics
MSC-class: 35A99; 35A30; 35K57; 35K05
Retrieve: 0803.1156
Journal: J. Math. Phys. 49, 103506 (2008) (34 pages).

[J25] Foundations of the calculus of variations in generalized function algebras.
with S. Konjik and M. Oberguggenberger
Subj-class: Functional Analysis, Global Analysis
MSC-class: 49J27, 46F30, 49K27, 37K05
Retrieve: 0707.1842 [abs, pdf, other]
Journal: Acta Appl. Math. 103: 169-199, 2008.

[J24] Conservation Laws and Potential Symmetries of Linear Parabolic Equations.
with R. Popovych and N. Ivanova
Subj-class: Symmetry group analysis of PDEs; Mathematical Physics
MSC-class: 35A30; 35Q55;58J70;35C05
Retrieve: 0706.0443 [abs, pdf, other]
Journal: Acta Appl. Math., 100, Number 2, 113-185, 2008.

[J23] Sheaves of nonlinear generalized functions and manifold-valued distributions.
with R. Steinbauer and J. Vickers
Subj-class: Functional Analysis, Differential Geometry.
MSC-class: 46F30, 53B20, 46T30
Retrieve: math.FA/0609358 [abs, src, pdf, other]
Journal: Trans. Amer. Math. Soc. 361, 5177-5192, 2009.

[J22] Generalized solutions of the Vlasov-Poisson system with singular data.
with I. Kmit, R. Steinbauer
Subj-class: Analysis of PDEs; Mathematical Physics
MSC-class: 35A05; 46F30, 35Q72, 82C22
Retrieve: math.AP/0601552 [abs, src, pdf, other]
Journal: J. Math. Anal. Appl., 340, No. 1, 575-587, 2008.

[J21] Generalized Group Actions in a Global Setting.
with S. Konjik
Subj-class: Functional Analysis, Differential Geometry
MSC-class: 46F30; 58D19
Retrieve: math.DG/0412045 [abs, src, pdf, other]
Journal: J. Math. Anal. Appl., 322, 420-436, 2006.

[J20] Group invariants in algebras of generalized functions.
with S. Konjik
Subj-class: Functional Analysis, Differential Geometry
MSC-class: 46F30; 58D19; 46T30; 35A30
Retrieve: math.DG/0412045 [abs, src, pdf, other]
Journal: Integral Transforms Spec. Funct., 17, No.2-3, 77-84, 2006.

[J19] Global Gronwall Estimates for Integral Curves on Riemannian Manifolds.
with H. Schichl, R. Steinbauer and J. A. Vickers
Subj-class: Differential Geometry
MSC-class: 53B21; 53C22; 34A26
Retrieve: math.DG/0412045 [abs, src, pdf, other]
Journal: Rev. Mat. Complut., no. 1, 133--137, 2006.

[J18] On Local Solutions of the Relativistic Vlasov-Klein-Gordon system.
with G. Rein, R. Steinbauer and G. Teschl
Subj-class: Partial Differential Equations
MSC-class: 35A07; 35Q72; 35Q40; 82C22
Retrieve: math.AP/0407028 [abs, src, pdf, other]
Journal: Electron. J. Diff. Eqns., Vol. 2005, No. 01, 1-17, 2005.

[J17] Generalized connections and curvature.
with R. Steinbauer and J. Vickers
Subj-class: Functional Analysis, Differential Geometry, Mathematical Physics.
MSC-class: 46F30, 53B05, 46T30
Retrieve: math.FA/0403040 [abs, src, pdf, other]
Journal: Math. Proc. Cambridge Philos. Soc., 139, no. 3, 497--521, 2005.

[J16] Non-smooth differential geometry and algebras of generalized functions.
Subj-class: Functional Analysis, Global Analysis.
MSC-class: 46F30, 53B20, 46T30
Retrieve: math.FA/0312487 [abs, src, pdf, other]
Journal: J. Math. Anal. Appl. 297, 456-471, 2004.

[J15] Generalized flows and singular ODEs on differentiable manifolds.
with M. Oberguggenberger, R. Steinbauer and J. Vickers
Subj-class: Functional Analysis, Global Analysis.
MSC-class: 46F30, 53B20, 46T30
Retrieve: math.FA/0304131 [abs, src, pdf, other]
Journal: Acta Appl. Math. 80, 221-241, 2004.

[J14] Global weak solutions of the relativistic Vlasov-Klein-Gordon System.
with G. Rein, R. Steinbauer and G. Teschl
Subj-class: Partial Differential Equations
MSC-class: 35D05, 35Q72
Retrieve: math.AP/0209303 [abs, src, pdf, other]
Journal: Comm. Math. Phys. 238 (1-2), 367-378, 2003.

[J13] Intrinsic characterization of manifold-valued generalized functions.
with R. Steinbauer and J. Vickers
Subj-class: Functional Analysis, Global Analysis.
MSC-class: 46F30, 53B20, 46T30
Retrieve: math.FA/0205223 [abs, src, pdf, other]
Journal: Proc. London Math. Soc., 87 (2), 451-470, 2003.

[J12] Generalized pseudo-Riemannian Geometry.
with R. Steinbauer
Subj-class: Functional Analysis, Mathematical Physics.
MSC-class: 46F30, 46T30
Retrieve: math.FA/0107057 [abs, src, pdf, other]
Journal: Trans. Amer. Math. Soc. 354, no. 10, 4179-4199, 2002.

[J11] Generalized functions valued in a smooth manifold.
Subj-class: Functional Analysis, Global Analysis.
MSC-class: 46F30, 53B20, 46T30
Retrieve: math.FA/0107051 [abs, src, pdf, other]
Journal: Monatsh. Math., 137, 31-49, 2002.

[J10] Symmetry group analysis of weak solutions.
with N. Dapic and S. Pilipovic
Subj-class: Differential Equations, Lie Group Actions, Generalized Functions
MSC-class: 46F30; 58D19
Retrieve: math.FA/0104055 [abs, src, pdf, other]
Journal: Proc. London Math. Soc. 84 (3), 686-710, 2002.

[J9] Foundations of a nonlinear distributional geometry.
with R. Steinbauer
Subj-class: Functional Analysis, Mathematical Physics.
MSC-class: 46F30;46T30;46F10;37J05
Retrieve: math.FA/0102019 [abs, src, pdf, other]
Journal: Acta Appl. Math. 71, 179-206, 2002.

[J8] A Global Theory of Algebras of Generalized Functions.
with M. Grosser, R. Steinbauer and J. Vickers
Subj-class: Functional Analysis; Mathematical Physics
MSC-class: 46F30; 46T30
Report: ESI-Preprint 813
Retrieve: math.FA/9912216 [abs, src, pdf, other]
Journal: Advances in Math. 166, No. 1, 50-72, 2002 .

[J7] Microlocal properties of basic operations in Colombeau algebras.
with G. Hörmann
Subj-class: Functional Analysis
MSC-class: 46F30; 35A21
Retrieve: math.FA/0008206 [abs, src, pdf, other]
Journal: J. Math. Anal. Appl. 261, 254-270, 2001.

[J6] Group Analysis of Differential Equations and Generalized Functions
with M. Oberguggenberger
Subj-class: Functional Analysis; Analysis of PDEs
MSC-class: 46F30; 35Dxx; 35A30; 58G35
Report: math.FA/9912217 [abs, src, pdf, other]
Journal: SIAM J. Math. Anal. 31 (2000) no. 6, 1192-1213.

[J5] Regularized derivatives in a 2-dimensional model of self-interacting fields with singular data
with G. Hörmann
Subj-class: Analysis of PDEs; Functional Analysis
MSC-class: 35Dxx; 46F10; 35Lxx; 78A25
Retrieve: math.FA/9912219 [abs, src, pdf, other]
Journal: Zeitschr. Anal. u. Anw. 19, Nr 1 (2000), 147-158

[J4] A note on the Penrose junction conditions.
with R. Steinbauer
Subj-class: General Relativity and Quantum Cosmology; Mathematical Physics
MSC-class: 83Cxx; 46F10; 83C35; 35Dxx
Journal-ref: Class. Quant. Grav. 16 (1999) 1255-1264
Report: ESI-Preprint 627.
Retrieve: gr-qc/9811007 [abs, src, pdf, other]
Journal: Classical and Quantum Gravity 16 (1999), 1255-1264,
This article was featured among the highlights of 1999 and 2000 in Classical and Quantum Gravity.

[J3] A rigorous solution concept for geodesic and geodesic deviation equations
in impulsive wave geometries.

with R. Steinbauer
Subj-class: General Relativity and Quantum Cosmology; Mathematical Physics
MSC-class: 83C35; 83C99; 46F10; 35Dxx
Report: ESI-Preprint 558.
Retrieve: gr-qc/9806009 [abs, src, pdf, other]
Journal: Journal of Mathematical Physics Vol. 40, Nr 3 (1999), 1479 - 1489.

[J2] Characterization of Colombeau Generalized Functions by their Pointvalues
with M. Oberguggenberger
Subj-class: Functional Analysis;
MSC-class: 46F10; 03H05; 35Dxx
Retrieve: point values
Journal: Math. Nachr. 203 (1999), 147-157.

[J1] Nonlinearity and Self-Interaction in Physical Field Theories with Singularities
with G. Hörmann
Subj-class: Functional Analysis;Analysis of PDEs.
MSC-class: 35Dxx, 46F10,35Qxx,78A25,35Q60.
Journal: Integral Transf. Special Funct., Vol. 6, No.1-4 (1997), 190-199.


Contributions to Proceedings

[P10] Inverse Function Theorems for Generalized Smooth Functions
with P. Giordano
Subj-class: Functional Analysis
MSC-class:46F30, 26E30
Retrieve: 1602.00013
In: M. Oberguggenberger, J. Toft, J. Vindas, P. Wahlberg, Generalized Functions and Fourier Analysis, Springer, 2017, pp 95 - 114.

[P9] A regularization approach to non-smooth symplectic geometry
with G. Hörmann and S. Konjik
Subj-class: Differential Geometry
MSC-class: 53D05, 46F30
Retrieve: 1403.0234
Journal: Operator Theory: Advances and Applications, Birkäuser, Basel, to appear.

[P8] Geometric regularization on Riemannian and Lorentzian manifolds
with S. Dave and G. Hörmann
Subj-class: Global Analysis
MSC-class: 58J40, 58J47, 58J42
Retrieve: 1107.0010
Journal: M. Ruzhansky, J. Wirth (Eds.) Evolution Equations of Hyperbolic and Schrödinger Type, Progress in Mathematics 301, Birkäuser, 87-102, 2012.

[P7] Wave equations on non-smooth space-times
with G. Hörmann and R. Steinbauer
Subj-class: Analyis of PDEs
MSC-class: 58J45, 35L05, 35L15, 35D99, 46F30
Retrieve: 1107.0014
Journal: M. Ruzhansky, J. Wirth (Eds.) Evolution Equations of Hyperbolic and Schrödinger Type, Progress in Mathematics 301, Birkäuser, 163-186, 2012.

[P6] Is a nonclassical symmetry a symmetry?
with R. Popovych
Subj-class: Symmetry group analysis of PDEs; Mathematical Physics
MSC-class: 35A30, 35C05
Retrieve: 0903.0821
Journal: Proceedings of 4th Workshop "Group Analysis of Differential Equations and Integrable Systems" (26-30 October 2008, Protaras, Cyprus), 2009, 107-120

[P5] Recent progress in special Colombeau algebras: geometry, topology, and algebra
Subj-class: Functional Analysis, Differential Geometry, Algebra
MSC-class: 46F30, 46T30, 46A20, 16D25, 53B20
Retrieve: 0712.4340
Journal: Banach Center Publications 88, 175-184, 2010.

[P4] Diffeomorphism invariant Colombeau algebras. Part III: Global theory.
Subj-class: Functional Analysis; Mathematical Physics
MSC-class: 46F30; 46T30
Retrieve: math.FA/0104272 [abs, src, pdf, other]
in: 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 117-126, 2004.

[P3] Diffeomorphism invariant construction of nonlinear generalized functions
with M. Grosser, R. Steinbauer, H. Urbantke, and J. Vickers, Ann. Phys. 9 Spec. Issue, SI-173-SI-174.

[P2] Lie Symmetries of Differential Equations in a Generalized Functions Setting.
in: M. Grosser, G. Hörmann, M. Kunzinger, M. Oberguggenberger (Eds.),
Nonlinear Theory of Generalized Functions, CRC Research Notes in Mathematics 401, 241-250, (1999).

[P1] Symmetries of Differential Equations in Colombeau Algebras.
with M. Oberguggenberger
in: N. H. Ibragimov, F. M. Mahomed (Eds.), Modern Group Analysis VI, New Age Int. Publ., 9-20, (1997).


Preprints

[Pre1] Lorentzian length spaces
with C. Sämann
Subj-class: Differential Geometry, Metric Geometry, General Relativity and Quantum Cosmology
MSC-class: 53C23, 53C50, 53B30, 53C80
Retrieve: 1711.08990


Editorial Activities

[E2] Topics in Partial Differential Equations, Harmonic Analysis, and Geometry
with M. Grosser, S. Pilipovic and R. Steinbauer
Proceedings of the International Conference on Generalized Functions GF2009, Vienna, August 31-September 4, 2009
Integral Transforms Spec. Funct. 22 (2011), no. 4-5.

[E1] Nonlinear Theory of Generalized Functions.
with M. Grosser, G. Hörmann and M. Oberguggenberger
Proceedings of a Workshop held at ESI, Oct.-Dec. 1997,
CRC Research Notes in Mathematics 401 (1999).
ISBN 0849306493.
Last modified November 27, 2017 by Michael Kunzinger.