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1997 | 126 | 2 | 161-170
Tytuł artykułu

Perfect sets of finite class without the extension property

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that generalized Cantor sets of class α, α ≠ 2 have the extension property iff α < 2. Thus belonging of a compact set K to some finite class α cannot be a characterization for the existence of an extension operator. The result has some interconnection with potential theory.
Słowa kluczowe
Czasopismo
Rocznik
Tom
126
Numer
2
Strony
161-170
Opis fizyczny
Daty
wydano
1997
otrzymano
1997-01-07
poprawiono
1997-05-26
Twórcy
autor
  • Department of Mathematics, Bilkent University, 06533 Ankara, Turkey , goncha@fen.bilkent.edu.tr
  • Department of Mathematics, Civil Engineering University, Rostov-na-Donu, Russia
Bibliografia
  • [1] L. Białas-Cież, Equivalence of Markov's property and Hölder continuity of the Green function for Cantor-type sets, East J. Approx. 1 (1995), 249-253.
  • [2] E. Bierstone, Extension of Whitney fields from subanalytic sets, Invent. Math. 46 (1978), 277-300.
  • [3] A. Goncharov, A compact set without Markov's property but with an extension operator for $C^∞$ functions, Studia Math. 119 (1996), 27-35.
  • [4] A. Goncharov and M. Kocatepe, Isomorphic classification of the spaces of Whitney functions, to appear.
  • [5] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, 5th ed., Academic Press, 1994.
  • [6] W. K. Hayman and P. B. Kennedy, Subharmonic Functions, Academic Press, 1976.
  • [7] N. S. Landkof, Foundations of Modern Potential Theory, Nauka, Moscow, 1966 (in Russian).
  • [8] R. Meise und D. Vogt, Einführung in die Funktionalanalysis, Vieweg, 1992.
  • [9] B. S. Mityagin, Approximative dimension and bases in nuclear spaces, Russian Math. Surveys 16 (4) (1961), 59-127.
  • [10] R. Nevanlinna, Analytic Functions, Springer, 1970.
  • [11] Z. Ogrodzka, On simultaneous extension of infinitely differentiable functions, Studia Math. 28, (1967), 193-207.
  • [12] W. Pawłucki and W. Pleśniak, Markov's inequality and $C^∞$ functions on sets with polynomial cusps, Math. Ann. 275, (1986), 467-480.
  • [13] W. Pleśniak, A Cantor regular set which does not have Markov's property, Ann. Polon. Math. 51 (1990), 269-274.
  • [14] R. T. Seeley, Extension of $C^∞$ functions defined in a half space, Proc. Amer. Math. Soc. 15 (1964), 625-626.
  • [15] J. Siciak, Compact sets in $ℝ^n$ admitting polynomial inequalities, Trudy Mat. Inst. Steklov. 203 (1994), 441-448.
  • [16] M. Tidten, Fortsetzungen von $C^∞$-Funktionen, welche auf einer abgeschlossenen Menge in $ℝ^n$ definiert sind, Manuscripta Math. 27 (1979), 291-312.
  • [17] M. Tidten, Kriterien für die Existenz von Ausdehnungsoperatoren zu E(K) für kompakte Teilmengen K von ℝ, Arch. Math. (Basel) 40 (1983), 73-81.
  • [18] D. Vogt, Charakterisierung der Unterräume von s, Math. Z. 155 (1977), 109-117.
  • [19] V. P. Zahariuta, Some linear topological invariants and isomorphisms of tensor products of scale's centers, Izv. Sev. Kavkaz. Nauch. Tsentra Vyssh. Shkoly 4 (1974), 62-64 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv126i2p161bwm
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