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1996 | 69 | 2 | 271-274
Tytuł artykułu

On Ditkin sets

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the study of spectral synthesis S-sets and C-sets (see Rudin [3]; Reiter [2] uses the terminology Wiener sets and Wiener-Ditkin sets respectively) have been discussed extensively. A new concept of Ditkin sets was introduced and studied by Stegeman in [4] so that, in Reiter's terminology, Wiener-Ditkin sets are precisely sets which are both Wiener sets and Ditkin sets. The importance of such sets in spectral synthesis and their connection to the C-set-S-set problem (see Rudin [3]) are mentioned there. In this paper we study local properties, unions and intersections of Ditkin sets. (Warning: Usually in the literature "Ditkin set" means "C-set", but we follow the terminology of Stegeman.) Our results include: (i) if each point of a closed set E has a closed relative Ditkin neighbourhood, then E is a Ditkin set; (ii) any closed countable union of Ditkin sets is a Ditkin set; (iii) if $E_1 ∩ E_2$ is a Ditkin set, then $E_1 ∩ E_2$ is a Ditkin set if and only if $E_1$ and $E_2$ are Ditkin sets; and (iv) if $E_1, E_2$ are Ditkin sets with disjoint boundaries then $E_1 ∩ E_2$ is a Ditkin set.
Słowa kluczowe
Rocznik
Tom
69
Numer
2
Strony
271-274
Opis fizyczny
Daty
wydano
1996
otrzymano
1994-09-12
poprawiono
1995-02-15
Twórcy
  • Ramanujan Institute, University of Madras, Madras 600 005, India
Bibliografia
  • [1] T. K. Muraleedharan and K. Parthasarathy, On unions and intersections of sets of synthesis, Proc. Amer. Math. Soc., to appear.
  • [2] H. Reiter, Classical Harmonic Analysis and Locally Compact Groups, Oxford University Press, Oxford, 1968.
  • [3] W. Rudin, Fourier Analysis on Groups, Interscience, New York, 1962.
  • [4] J. D. Stegeman, Some problems on spectral synthesis, in: Proc. Harmonic Analysis (Iraklion, 1978), Lecture Notes in Math. 781, Springer, Berlin, 1980, 194-203.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv69i2p271bwm
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