Eduard A. Nigsch

Personal Information

Mailing Address:Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
Room number: 03.135
Phone: +43 1 4277 50760
E-Mail: eduardREMOVE.nigsch@univie.REMOVEac.at

A CV is available here.

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:

Teaching

For a list of my teaching activities at the University of Vienna, see also here.

Research

My main research interests are algebras of nonlinear generalized functions, topological tensor products, and nonlinear (stochastic) PDEs.

Publications

All my publications are also available via arXiv.

Preprints

  1. M. Kunzinger, E. A. Nigsch and N. Ortner. “Laplace transformation of vector-valued distributions and applications to Cauchy-Dirichlet problems“. Submitted, 2018.
  2. E. A. Nigsch. “On spacetimes with distributional metric and curvature”. Preprint, 2018.
  3. N. Konatar, D. Mitrović and E. A. Nigsch. “Well-posedness for stochastic conservation laws on Riemannian manifolds”. Preprint, 2018.
  4. E. A. Nigsch. “On association in Colombeau algebras without asymptotics”. To appear, 2018.
  5. C. Bargetz, E. A. Nigsch, and N. Ortner. “Description of the \(\kappa\)-topologies on the spaces \(\mathcal{D}_{L^p}\), \(L^p\), \(\mathcal{M}^1\) by 'function'-seminorms”. Submitted, 2017. arXiv: 1711.06577.

Published Articles

  1. A. Debrouwere and E. A. Nigsch. “Sheaves of nonlinear generalized function spaces”. To appear in New York J. Math., 2017. arXiv: 1707.01568.
  2. E. A. Nigsch. “Colombeau Algebras without asymptotics”. To appear in Journal of Pseudo-Differential Operators and Applications, 2017. arXiv: 1704.08167.
  3. M. Grosser and E. A. Nigsch. “Full and special Colombeau Algebras”. To appear in Proc. Edinb. Math. Soc., 2017. arXiv: 1611.06061.
  4. E. A. Nigsch and N. Ortner. “A survey on duals of topological tensor products”. To appear in Rend. Sem. Mat. Univ. Politec. Torino, 2017. arXiv: 1604.02846.
  5. C. Bargetz, E. A. Nigsch, and N. Ortner. “Convolvability and regularization of distributions”. Annali di Matematica Pura ed Applicata (2017). doi: 10.1007/s10231-017-0662-3. arXiv: 1505.04599.
  6. 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. (2017), doi: 10.1007/s13398-016-0371-6. arXiv: 1604.02846.
  7. E. A. Nigsch. “Nonlinear generalized sections and vector bundle homomorphisms in Colombeau spaces of generalized functions”. Math. Nachr. (2017). doi: 10.1002/mana.201600088. arXiv: 1603.08347.
  8. 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.
  9. E. A. Nigsch. “Nonlinear generalized sections of vector bundles”. J. Math. Anal. Appl. 440 (2016), pp. 183–219. issn: 0022-247X. doi: 10.1016/j.jmaa.2016.03.022. arXiv: 1409.2962.
  10. E. A. Nigsch. “On regularization of vector distributions on manifolds”. Forum Math. (2016). To appear. issn: 0933-7741. doi: http://dx.doi.org/10.1515/forum-2015-0067. arXiv: 1504.02237.
  11. P. Giordano and E. A. Nigsch. “Unifying order structures for Colombeau algebras”. Math. Nachr. 288.11-12 (2015), pp. 1286–1302. issn: 0025-584X. doi: 10.1002/mana.201400277. arXiv: 1408.1242.
  12. 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. issn: 0013-0915. doi: 10.1017/S0013091514000091. arXiv: 1303.3102.
  13. E. A. Nigsch. “Some extensions to the functional analytic approach to Colombeau algebras”. Novi Sad J. Math. 45.1 (2015), pp. 231–240. issn: 1450-5444. arXiv: 1604.02860.
  14. 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.
  15. E. A. Nigsch. “Nonlinear tensor distributions on Riemannian manifolds”. Rocky Mt. J. Math. 44.2 (2014), pp. 649–683. issn: 0035-7596. doi: 10.1216/RMJ-2014-44-2-649. arXiv: 1104.0829.
  16. E. A. Nigsch. “Bornologically isomorphic representations of distributions on manifolds”. Monatsh. Math. 170.1 (2013), pp. 49–63. issn: 0026-9255. doi: 10.1007/s00605-012-0442-5. arXiv: 1105.1642.
  17. 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. issn: 0025-584X. doi: 10.1002/mana.200910280. arXiv: 1104.0911.
  18. 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. issn: 1982-6907. arXiv: 1309.1451.
  19. 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.
  20. E. A. Nigsch. “Approximation properties of local smoothing kernels”. Integral Transforms Spec. Funct. 22.4-5 (2011), pp. 303–310. issn: 1065-2469. doi: 10.1080/10652469.2010.541043. arXiv: 1604.02871.
  21. 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).

Theses

  1. E. A. Nigsch. “A nonlinear theory of tensor distributions on Riemannian manifolds”. PhD thesis, University of Vienna, 2010. [PDF]
  2. E. A. Nigsch. “Colombeau generalized functions on manifolds”. Diploma thesis, Technical University of Vienna, 2006. [PDF]