Implicit functions from locally convex spaces to Banach spaces

Seppo Hiltunen

Studia Mathematica (1999)

  • Volume: 134, Issue: 3, page 235-250
  • ISSN: 0039-3223

Abstract

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We first generalize the classical implicit function theorem of Hildebrandt and Graves to the case where we have a Keller C Π k -map f defined on an open subset of E×F and with values in F, for E an arbitrary Hausdorff locally convex space and F a Banach space. As an application, we prove that under a certain transversality condition the preimage of a submanifold is a submanifold for a map from a Fréchet manifold to a Banach manifold.

How to cite

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Hiltunen, Seppo. "Implicit functions from locally convex spaces to Banach spaces." Studia Mathematica 134.3 (1999): 235-250. <http://eudml.org/doc/216636>.

@article{Hiltunen1999,
abstract = {We first generalize the classical implicit function theorem of Hildebrandt and Graves to the case where we have a Keller $C_Π^k$-map f defined on an open subset of E×F and with values in F, for E an arbitrary Hausdorff locally convex space and F a Banach space. As an application, we prove that under a certain transversality condition the preimage of a submanifold is a submanifold for a map from a Fréchet manifold to a Banach manifold.},
author = {Hiltunen, Seppo},
journal = {Studia Mathematica},
keywords = {implicit functions; locally convex spaces; Banach spaces},
language = {eng},
number = {3},
pages = {235-250},
title = {Implicit functions from locally convex spaces to Banach spaces},
url = {http://eudml.org/doc/216636},
volume = {134},
year = {1999},
}

TY - JOUR
AU - Hiltunen, Seppo
TI - Implicit functions from locally convex spaces to Banach spaces
JO - Studia Mathematica
PY - 1999
VL - 134
IS - 3
SP - 235
EP - 250
AB - We first generalize the classical implicit function theorem of Hildebrandt and Graves to the case where we have a Keller $C_Π^k$-map f defined on an open subset of E×F and with values in F, for E an arbitrary Hausdorff locally convex space and F a Banach space. As an application, we prove that under a certain transversality condition the preimage of a submanifold is a submanifold for a map from a Fréchet manifold to a Banach manifold.
LA - eng
KW - implicit functions; locally convex spaces; Banach spaces
UR - http://eudml.org/doc/216636
ER -

References

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  1. [1] A. Frölicher and W. Bucher, z Calculus in Vector Spaces without Norm, Lecture Notes in Math. 30, Springer, Berlin, 1966. Zbl0156.38303
  2. [2] A. Frölicher and A. Kriegl, z Linear Spaces and Differentiation Theory, Pure Appl. Math., Wiley, Chichester, 1988. 
  3. [3] M. W. Hirsch, Differential Topology, Springer, New York, 1976. 
  4. [4] H. H. Keller, z Differential Calculus in Locally Convex Spaces, Lecture Notes in Math. 417, Springer, Berlin, 1974. 
  5. [5] A. Kriegl, Eine kartesisch abgeschlossene Kategorie glatter Abbildungen zwischen beliebigen lokalkonvexen Vektorräumen, Monatsh. Math. 95 (1983), 287-309. 
  6. [6] A. Kriegl and P. W. Michor, z Aspects of the theory of infinite dimensional manifolds, Differential Geom. Appl. 1 (1991), 159-176. Zbl0782.58011
  7. [7] S. Lang, Differential Manifolds, Springer, New York, 1988. 
  8. [8] U. Seip, Kompakt erzeugte Vektorräume und Analysis, Lecture Notes in Math. 273, Springer, Berlin, 1972. Zbl0242.46003

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