Eduard A. Nigsch

Personal Information

Mailing Address:Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria
Room number: DA 06 L02


All my publications are also available via arXiv.


  1. E. A. Nigsch and J. A. Vickers. “Nonlinear generalised functions on manifolds“. Submitted, 2019. arXiv: 1910.03411.
  2. E. A. Nigsch and J. A. Vickers. “A nonlinear theory of distributional geometry“. Submitted, 2019. arXiv: 1910.03426.
  3. A. Debrouwere and E. A. Nigsch. “On the space of Laplace transformable distributions“. To appear in Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., 2020. arXiv: 1910.01388.
  4. N. Konatar, D. Mitrović and E. A. Nigsch. “Well-posedness for stochastic conservation laws on Riemannian manifolds”. Preprint, 2018. arXiv: 1809.01866.

Published or accepted Articles

  1. E. A. Nigsch. “Spacetimes with distributional semi-Riemannian metrics and their curvature“. Journal of Differential Geometry (2020). doi: 10.1016/j.geomphys.2020.103623. arXiv: 1902.06470.
  2. C. Bargetz, E. A. Nigsch, and N. Ortner. “A simpler description of the \(\kappa\)-topologies on the spaces \(\mathcal{D}_{L^p}\), \(L^p\), \(\mathcal{M}^1\) by 'function'-seminorms”. Math. Nachr. (2020), to appear. arXiv: 1711.06577.
  3. M. Kunzinger, E. A. Nigsch and N. Ortner. “Laplace transformation of vector-valued distributions and applications to Cauchy-Dirichlet problems“. J. Math. Anal. Appl. 478.2 (2019, pp. 990–1004. doi: 10.1016/j.jmaa.2019.06.002. arXiv: 1809.10444.
  4. E. A. Nigsch. “On association in Colombeau algebras without asymptotics”. K. Lindahl et al. (editors), Analysis, Probability, Applications, and Computation, Springer, 2019, pp. 437–443. arXiv: 1809.03865.
  5. A. Debrouwere and E. A. Nigsch. “Sheaves of nonlinear generalized function spaces”. New York J. Math. 23 (2017), pp. 1751–1789. arXiv: 1707.01568.
  6. E. A. Nigsch. “Colombeau Algebras without asymptotics”. Journal of Pseudo-Differential Operators and Applications 10.1 (2019), pp. 133–154. doi: 10.1007/s11868-017-0230-z. arXiv: 1704.08167.
  7. M. Grosser and E. A. Nigsch. “Full and special Colombeau Algebras”. Proc. Edinb. Math. Soc. 61.4 (2018). doi: 10.1017/S001309151800010X. arXiv: 1611.06061.
  8. E. A. Nigsch and N. Ortner. “A survey on duals of topological tensor products”. Rend. Sem. Mat. Univ. Politec. Torino 75.2 (2017), pp. 11–17. arXiv: 1604.02846.
  9. C. Bargetz, E. A. Nigsch, and N. Ortner. “Convolvability and regularization of distributions”. Annali di Matematica Pura ed Applicata 196.6 (2017), pp. 2239–2251. doi: 10.1007/s10231-017-0662-3. arXiv: 1505.04599.
  10. E. A. Nigsch and N. Ortner. “The space \(\dot{\mathcal{B}}'\) of distributions vanishing at infinity – duals of tensor products”. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 112 (2018), pp. 251–269. doi: 10.1007/s13398-016-0371-6. arXiv: 1604.02846.
  11. E. A. Nigsch. “Nonlinear generalized sections and vector bundle homomorphisms in Colombeau spaces of generalized functions”. Math. Nachr. 290.13 (2017), pp. 1991–2008. doi: 10.1002/mana.201600088. arXiv: 1603.08347.
  12. E. A. Nigsch. “On a nonlinear Peetre's theorem in full Colombeau algebras”. Comment. Math. Univ. Carol. 58.1 (2017), pp. 69–77. arXiv: 1601.06556.
  13. E. A. Nigsch. “Nonlinear generalized sections of vector bundles”. J. Math. Anal. Appl. 440 (2016), pp. 183–219. doi: 10.1016/j.jmaa.2016.03.022. arXiv: 1409.2962.
  14. E. A. Nigsch. “On regularization of vector distributions on manifolds”. Forum Math. 28.6 (2016), pp. 1131–1141. doi: arXiv: 1504.02237.
  15. P. Giordano and E. A. Nigsch. “Unifying order structures for Colombeau algebras”. Math. Nachr. 288.11–12 (2015), pp. 1286–1302. doi: 10.1002/mana.201400277. arXiv: 1408.1242.
  16. E. A. Nigsch. “A new approach to diffeomorphism invariant algebras of generalized functions”. Proc. Edinb. Math. Soc., II. Ser. 58.3 (2015), pp. 717–737. doi: 10.1017/S0013091514000091. arXiv: 1303.3102.
  17. E. A. Nigsch. “Some extensions to the functional analytic approach to Colombeau algebras”. Novi Sad J. Math. 45.1 (2015), pp. 231–240. arXiv: 1604.02860.
  18. E. A. Nigsch. “The functional analytic foundation of Colombeau algebras”. J. Math. Anal. Appl. 421.1 (2015), pp. 415–435. doi: 10.1016/j.jmaa.2014.07.014. arXiv: 1305.1460.
  19. E. A. Nigsch. “Nonlinear tensor distributions on Riemannian manifolds”. Rocky Mt. J. Math. 44.2 (2014), pp. 649–683. doi: 10.1216/RMJ-2014-44-2-649. arXiv: 1104.0829.
  20. E. A. Nigsch. “Bornologically isomorphic representations of distributions on manifolds”. Monatsh. Math. 170.1 (2013), pp. 49–63. doi: 10.1007/s00605-012-0442-5. arXiv: 1105.1642.
  21. E. A. Nigsch. “Point value characterizations and related results in the full Colombeau algebras \(\mathcal{G}^e(\Omega)\) and \(\mathcal{G}^d(\Omega)\)”. Math. Nachr. 286.10 (2013), pp. 1007–1021. doi: 10.1002/mana.200910280. arXiv: 1104.0911.
  22. E. A. Nigsch and C. Sämann. “Global algebras of nonlinear generalized functions with applications in general relativity”. São Paulo J. of Math. Sci. 7.2 (2013), pp. 143–171. arXiv: 1309.1451.
  23. M. Kunzinger and E. A. Nigsch. “Manifold-valued generalized functions in full Colombeau spaces”. Commentat. Math. Uni. Carol. 52.4 (2011), pp. 519–534. arXiv: 1103.5845.
  24. E. A. Nigsch. “Approximation properties of local smoothing kernels”. Integral Transforms Spec. Funct. 22.4–5 (2011), pp. 303–310. doi: 10.1080/10652469.2010.541043. arXiv: 1604.02871.
  25. F. Nigsch, A. Bender, B. van Buuren, E. A. Nigsch, J. Tissen and J. B. O. Mitchell. “Melting Point Prediction Employing k-Nearest Neighbor Algorithms and Genetic Parameter Optimization.” J. Chem. Inf. Model 46.6 (2006).