Universal prolongation of linear partial differential equations on filtered manifolds

Katharina Neusser

Archivum Mathematicum (2009)

  • Volume: 045, Issue: 4, page 289-300
  • ISSN: 0044-8753

Abstract

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The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.

How to cite

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Neusser, Katharina. "Universal prolongation of linear partial differential equations on filtered manifolds." Archivum Mathematicum 045.4 (2009): 289-300. <http://eudml.org/doc/250691>.

@article{Neusser2009,
abstract = {The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.},
author = {Neusser, Katharina},
journal = {Archivum Mathematicum},
keywords = {prolongation; partial differential equations; filtered manifolds; contact manifolds; weighted jet bundles; prolongation; partial differential equation; filtered manifold; contact manifold; weighted jet bundle},
language = {eng},
number = {4},
pages = {289-300},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Universal prolongation of linear partial differential equations on filtered manifolds},
url = {http://eudml.org/doc/250691},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Neusser, Katharina
TI - Universal prolongation of linear partial differential equations on filtered manifolds
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 4
SP - 289
EP - 300
AB - The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.
LA - eng
KW - prolongation; partial differential equations; filtered manifolds; contact manifolds; weighted jet bundles; prolongation; partial differential equation; filtered manifold; contact manifold; weighted jet bundle
UR - http://eudml.org/doc/250691
ER -

References

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  1. Beals, R., Greiner, P. C., Calculus on Heisenberg manifolds, Ann. of Math. Stud. 119 (1988), x+194 pp. (1988) Zbl0654.58033MR0953082
  2. Goldschmidt, H., 10.2307/1970689, Ann. Math. 86 (1967), 246–270. (1967) Zbl0154.35103MR0219859DOI10.2307/1970689
  3. Goldschmidt, H., Prolongations of linear partial differential equations: A conjecture of Élie Cartan, Ann. Sci. École Norm. Sup. (4) 1 (1968), 417–444. (1968) MR0235584
  4. Morimoto, T., HASH(0x1cef7a8) 
  5. Morimoto, T., Théorème de Cartan-Kähler dans une classe de fonctions formelles Gevrey, C. R. Acad. Sci. Paris Sér. A Math. 311 (1990), 443–436. (1990) Zbl0714.58060MR1075665
  6. Morimoto, T., Théorème d’existence de solutions analytiques pour des systèmes d’équations aux dérivées partielles non-linéaires avec singularités, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), 1491–1496. (1995) Zbl0842.22009MR1366107
  7. Morimoto, T., Lie algebras, geometric structures and differential equations on filtered manifolds, In “Lie Groups Geometric Structures and Differential Equations - One Hundred Years after Sophus Lie”, Adv. Stud. Pure Math., Math. Soc. of Japan, Tokyo, 2002, pp. 205–252. (2002) Zbl1048.58015MR1980903
  8. Spencer, D. C., 10.1090/S0002-9904-1969-12129-4, Bull. Amer. Math. Soc. 75 (1969), 179–239. (1969) Zbl0185.33801MR0242200DOI10.1090/S0002-9904-1969-12129-4
  9. Taylor, M. E., Noncommutative microlocal analysis I, Mem. Amer. Math. Soc. 52 (313) (1984), iv+182 pp. (1984) Zbl0554.35025MR0764508
  10. van Erp, E.,, The Atiyah-Singer index formula for subelliptic operators on contact manifolds. Part 1, To appear in Ann. of Math. preprint arXiv: 0804.2490. 

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