The Zahorski theorem is valid in Gevrey classes

• Autorzy: Jean Schmets , Manuel Valdivia
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Gevrey classes; defect point; divergence point

Kategorie tematyczne

• 26E05: Real-analytic functions
• 26E10: C ∞ -functions, quasi-analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1996
• Tom: 151
• Numer: 2
• Strony: 149-166

Daty

wydano

1996

otrzymano

1995-11-20

poprawiono

1996-04-25

Twórcy

autor

Jean Schmets

• Institut de Mathématique, Université de Liège, 15, avenue des Tilleuls, B-4000 Liège, Belgium

autor

Manuel Valdivia

• Facultad de Matemáticas, Universidad de Valencia, Dr. Moliner 50, E-46100 Burjasot (Valencia), Spain

Bibliografia

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• [2] S. Mandelbrojt, Séries entières et transformées de Fourier, Applications, Publ. Math. Soc. Japan 10, 1967.
• [3] H. Salzmann and K. Zeller, Singularitäten unendlich oft differenzierbarer Funktionen, Math. Z. 62 354-367 (1955).
• [4] J. Siciak, Punkty regularne i osobliwe funkcji klasy $C_∞$ [Regular and singular points of $C_∞$ 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).
• [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).