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2000 | 142 | 2 | 135-148
Tytuł artykułu

Representations of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We give a representation of the spaces $C^∞(ℝ^N) ∩ H^{k,p}(ℝ^N)$ as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that $C^∞(ℝ^N) ∩ H^{k,2}(ℝ^N)$ is isomorphic to the sequence space $s^{ℕ} ∩ l^2(l^2)$, thereby showing that the isomorphy class does not depend on the dimension N if p=2.
Słowa kluczowe
Czasopismo
Rocznik
Tom
142
Numer
2
Strony
135-148
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-02-19
poprawiono
2000-06-12
Twórcy
  • Dipartimento di Matematica 'E. De Giorgi', Università - C.P. 193, 73100 Lecce, Italy
  • Dipartimento di Matematica 'E. De Giorgi', Università - C.P. 193, 73100 Lecce, Italy
Bibliografia
  • [A] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
  • [AA] A. A. Albanese, Montel subspaces of Fréchet spaces of Moscatelli type, Glasgow Math. J. 39 (1997), 345-350.
  • [AMM1] A. A. Albanese, G. Metafune and V. B. Moscatelli, Representations of the spaces $C^m(Ω) ∩ H^{k,p}(Ω)$, Math. Proc. Cambridge Philos. Soc. 120 (1996), 489-498.
  • [AMM2] A. A. Albanese, G. Metafune and V. B. Moscatelli, Representations of the spaces $C^m(ℝ^N) ∩ H^{k,p}ℝ^N$, in: Functional Analysis (Trier, 1994), S. Dierolf, S. Dineen and P. Domański (eds.), Walter de Gruyter, 1996, 11-20.
  • [AMM3] A. A. Albanese, G. Metafune and V. B. Moscatelli, On the spaces $C^k(ℝ) ∩ L^p(ℝ)$, Arch. Math. (Basel) 68 (1997), 228-232.
  • [AM] A. A. Albanese and V. B. Moscatelli, A method of construction of Fréchet spaces, in: Functional Analysis, P. K. Jain (ed.), Narosa Publishing House, New Delhi, 1998, 1-8.
  • [BB] K. D. Bierstedt and J. Bonet, Stefan Heinrich's density condition for Fréchet spaces and the characterization of distinguished Köthe echelon spaces, Math. Nachr. 135 (1988), 149-180.
  • [B] J. Bonet, Intersections of Fréchet Schwartz spaces and their duals, Arch. Math. (Basel) 68 (1997), 320-325.
  • [BD] J. Bonet and S. Dierolf, Fréchet spaces of Moscatelli type, Rev. Mat. Univ. Complut. Madrid 2 (suppl.) (1989), 77-92.
  • [BT] J. Bonet and J. Taskinen, Non-distinguished Fréchet function spaces, Bull. Soc. Roy. Sci. Liège 58 (1989), 483-490.
  • [DK] S. Dierolf and Khin Aye Aye, On projective limits of Moscatelli type, in: Functional Analysis (Trier, 1994), S. Dierolf, S. Dineen and P. Domański (eds.), Walter de Gruyter, 1996, 105-118.
  • [MT] P. Mattila and J. Taskinen, Remarks on bases in a Fréchet function space, Rev. Mat. Univ. Complut. Madrid 6 (1993), 93-99.
  • [M] V. B. Moscatelli, Fréchet spaces without continuous norms and without bases, Bull. London Math. Soc. 12 (1980), 63-66.
  • [S] R. T. Seeley, Extension of $C^∞$ functions defined in a half space, Proc. Amer. Math. Soc. 15 (1964), 625-626.
  • [T1] J. Taskinen, A continuous surjection from the unit interval onto the unit square, Rev. Mat. Univ. Complut. Madrid 6 (1993), 101-120.
  • [T2] J. Taskinen, Examples of non-distinguished Fréchet spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 14 (1989), 75-88.
  • [V1] M. Valdivia, Topics in Locally Convex Spaces, North-Holland Math. Stud. 67, 1982.
  • [V2] M. Valdivia, A characterization of totally reflexive Fréchet spaces, Math. Z. 200 (1989), 327-346.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv142i2p135bwm
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