# The Zahorski theorem is valid in Gevrey classes

Fundamenta Mathematicae (1996)

- Volume: 151, Issue: 2, page 149-166
- ISSN: 0016-2736

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topSchmets, Jean, and Valdivia, Manuel. "The Zahorski theorem is valid in Gevrey classes." Fundamenta Mathematicae 151.2 (1996): 149-166. <http://eudml.org/doc/212187>.

@article{Schmets1996,

abstract = {Let Ω,F,G be a partition of $ℝ^n$ such that Ω is open, F is $F_σ$ and of the first category, and G is $G_δ$. We prove that, for every γ ∈ ]1,∞[, there is an element of the Gevrey class Γγ which is analytic on Ω, has F as its set of defect points and has G as its set of divergence points.},

author = {Schmets, Jean, Valdivia, Manuel},

journal = {Fundamenta Mathematicae},

keywords = {Gevrey classes; defect point; divergence point; -functions; Gevrey functions; multivariate Zahorski theorem; Gevrey class},

language = {eng},

number = {2},

pages = {149-166},

title = {The Zahorski theorem is valid in Gevrey classes},

url = {http://eudml.org/doc/212187},

volume = {151},

year = {1996},

}

TY - JOUR

AU - Schmets, Jean

AU - Valdivia, Manuel

TI - The Zahorski theorem is valid in Gevrey classes

JO - Fundamenta Mathematicae

PY - 1996

VL - 151

IS - 2

SP - 149

EP - 166

AB - Let Ω,F,G be a partition of $ℝ^n$ such that Ω is open, F is $F_σ$ and of the first category, and G is $G_δ$. We prove that, for every γ ∈ ]1,∞[, there is an element of the Gevrey class Γγ which is analytic on Ω, has F as its set of defect points and has G as its set of divergence points.

LA - eng

KW - Gevrey classes; defect point; divergence point; -functions; Gevrey functions; multivariate Zahorski theorem; Gevrey class

UR - http://eudml.org/doc/212187

ER -

## References

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- [2] S. Mandelbrojt, Séries entières et transformées de Fourier, Applications, Publ. Math. Soc. Japan 10, 1967. Zbl0172.09302
- [3] H. Salzmann and K. Zeller, Singularitäten unendlich oft differenzierbarer Funktionen, Math. Z. 62 354-367 (1955). Zbl0064.29903
- [4] J. Siciak, Punkty regularne i osobliwe funkcji klasy ${C}_{\infty}$ [Regular and singular points of ${C}_{\infty}$ functions], Zeszyty Nauk. Polit. Śląsk. Ser. Mat.-Fiz. 48 (853) (1986), 127-146 (in Polish).
- [5] H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 63-89 (1934). Zbl0008.24902
- [6] Z. Zahorski, Sur l'ensemble des points singuliers d'une fonction d'une variable réelle admettant les dérivées de tous les ordres, Fund. Math. 34 183-245(1947). Zbl0033.25504

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