Whitney ’ S Problem on Extendability of Functions and an Intrinsic Metric

@inproceedings{Zobin2003WhitneyS,
  title={Whitney ’ S Problem on Extendability of Functions and an Intrinsic Metric},
  author={Nahum Zobin},
  year={2003}
}
  • Nahum Zobin
  • Published 2003
We consider the space of functions with bounded (k + 1)-th derivatives in a general domain in Rn. Is every such function extendible to a function of the same class defined on the whole Rn? H.Whitney showed that the equivalence of the intrinsic (=geodesic) metric in this domain to the Euclidean one is sufficient for such extendability. There was an old conjecture (going back to H.Whitney) that this equivalence is also necessary for extendability. We disprove this conjecture and construct… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 17 references

Generalization of Whitney’s extension theorem

Yu. Brudnyi, P. A. Shvartsman
Intern. Math. Res. Notes • 1994

Shvartsman , Generalization of Whitney ’ s extension theorem , Intern

P. A. Yu. Brudnyi
Math . Res . Notes • 1994

Whitney ’ s extension theorem for nonquasianalytic classes of ultradifferentiable functions

R. W. Braun, R. Meise, B. A. Taylor
Studia Math . • 1991

Whitney’s extension theorem for nonquasianalytic classes of ultradifferentiable functions, Studia Math

J. Bonèt, R. W. Braun, R. Meise, B. A. Taylor
1991
View 1 Excerpt

A linear extension operator for a space of smooth functions defined on a closed subset of R n , ( Russian ) , Dokl

P. A. Shvartsman Yu. Brudnyi
Akad . Nauk SSSR • 1985

A linear extension operator for a space of smooth functions defined on a closed subset of Rn, (Russian)

Yu. Brudnyi, P. A. Shvartsman
Dokl. Akad. Nauk SSSR • 1985

Description of traces of some classes of functions of several variables, Preprint #84.21

V. N. Konovalov
Institute of Mathematics, Academy of Sciences of Ukraine • 1984
View 1 Excerpt

Function spaces on subsets of Rn, Math

A. Jonsson, H. Wallin
Reports, 1, vol. 2, • 1984
View 1 Excerpt

Quasiconformal mappings and extendability of functions in Sobolev spaces

P. W. Jones
Acta Mathematica • 1981
View 1 Excerpt

Vodop’yanov, Criteria for extension of functions of the class L12 from unbounded plain domains, Siber

V. M. Gol’dshtein, S.K.T.G. Latfullin
Math. J.(English translation) • 1979
View 1 Excerpt

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