Personal Homepage of Eduard A. Nigsch

Contact Information

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

Thesis supervision

If you are interested in writing a bachelor's or master's thesis under my supervision, feel free to contact me for possible topics including but not limited to: Some approximate guidelines for writing a bachelor's thesis can be found here. There are also some specific topics for bachelor's theses.





Lecture notes


Almost all of my publications are also available via arXiv.

Published Articles

  1. C. Bargetz, E. A. Nigsch and N. Ortner. “Projective descriptions of spaces of functions and distributions”. Math. Nachr. (2023). doi: 10.1002/mana.202100526. arXiv: 2109.14448.
  2. C. Bargetz, A. Debrouwere and E. A. Nigsch. “Sequence space representations for spaces of smooth functions and distributions via Wilson bases”. Proc. Amer. Math. Soc. 150 (2022), pp. 3841-3852. doi: 10.1090/proc/15895. arXiv: 2107.00245.
  3. 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. 293.9 (2020), pp. 1691–1706. doi: 10.1002/mana.201900109. arXiv: 1711.06577.
  4. A. Debrouwere and E. A. Nigsch. “On the space of Laplace transformable distributions“. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 114.4 (2020). Id/No 185. doi: 10.1007/s13398-020-00907-2. arXiv: 1910.01388.
  5. E. A. Nigsch and J. A. Vickers. “Nonlinear generalized functions on manifolds“. Proc. R. Soc. A 476.2244 (2020). Id/No 20200640. doi: 10.1098/rspa.2020.0640. arXiv: 1910.03411.
  6. E. A. Nigsch. “Spacetimes with distributional semi-Riemannian metrics and their curvature“. J. Geom. Phys. 151 (2020). Id/No 103623. doi: 10.1016/j.geomphys.2020.103623. arXiv: 1902.06470.
  7. E. A. Nigsch and J. A. Vickers. “A nonlinear theory of distributional geometry“. Proc. R. Soc. A 476.2244 (2020). Id/No 20200642. doi: 10.1098/rspa.2020.0642. arXiv: 1910.03426.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. A. Debrouwere and E. A. Nigsch. “Sheaves of nonlinear generalized function spaces”. New York J. Math. 23 (2017), pp. 1751–1789. arXiv: 1707.01568.
  17. 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.
  18. 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.
  19. E. A. Nigsch. “On regularization of vector distributions on manifolds”. Forum Math. 28.6 (2016), pp. 1131–1141. doi: arXiv: 1504.02237.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. 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).