대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제26권2호
  • /
  • Pages.215-227
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  • 2011
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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WEAKLY SUFFICIENT SETS FOR WEIGHTED SPACES hΦ-∞(B)

  • Khoi, Le Hai (Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University (NTU))
  • 투고 : 2009.07.07
  • 심사 : 2011.01.07
  • 발행 : 2011.04.30
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초록

In this paper we introduce a class $h^{-\infty}_{\Phi}(\mathbb{B})$ of weighted spaces of harmonic functions in the unit ball $\mathbb{B}$ of $\mathbb{R}^n$. We dene weakly sufficient sets in this space and give an explicit construction of countable sets of such a type. Various examples of weight functions are also discussed.

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참고문헌

  1. A. V. Abanin, On some criteria of weak sufficiency, Math. Notes 40 (1986), no. 3-4, 757-764. https://doi.org/10.1007/BF01159666
  2. D. H. Armitage and S. J. Gardiner, Classical Potential Theory, Springer, London, 2001.
  3. S. R. Bell, A duality theorem for harmonic functions, Michigan Math. J. 29 (1982), no. 1, 123-128. https://doi.org/10.1307/mmj/1029002622
  4. J. Bonet and P. Domanski, Sampling sets and sufficient sets for $A^{\-}^{\infty}$, J. Math. Anal. Appl. 277 (2003), no. 2, 651-669. https://doi.org/10.1016/S0022-247X(02)00616-9
  5. L. Ehrenpreis, Analytically uniform spaces and some applications, Trans. Amer. Math. Soc. 101 (1961), 52-74. https://doi.org/10.1090/S0002-9947-1961-0131756-3
  6. C. Horowitz, B. Korenblum, and B. Pinchuk, Sampling sequences for $A^{\-}^{\infty}$, Michigan Math. J. 44 (1997), no. 2, 389-398. https://doi.org/10.1307/mmj/1029005713
  7. L. H. Khoi, Espaces conjugues ensembles faiblement suffisants discrets et systemes de representation exponentielle, Bull. Sci. Math. 113 (1989), no. 3, 309-347.
  8. Ju. F. Korobeinik, Representative systems, Math. USSR-Izv. 12 (1978), no. 2, 309-335. https://doi.org/10.1070/IM1978v012n02ABEH001856
  9. Ju. F. Korobeinik, Representative systems, Uspekhi Mat. Nauk 36 (1981), 73-126.
  10. B. M. Makarov, Inductive limits of normed spaces, Vestnik Leningrad. Univ. 20 (1965), no. 13, 50-58.
  11. D. M. Schneider, Sufficient sets for some spaces of entire functions, Trans. Amer. Math. Soc. 197 (1974), 161-180. https://doi.org/10.1090/S0002-9947-1974-0357835-2
  12. A. Shlapunov and N. Tarkhanov, Duality by repreducing kernels, Int. J. Math. Math. Sci. 2003 (2003), no. 6, 327-395. https://doi.org/10.1155/S0161171203206037
  13. E. J. Straube, Harmonic and analytic functions admitting a distribution boundary value, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 11 (1984), no. 4, 559-591.
  14. B. A. Taylor, Discrete sufficient sets for some spaces of entire functions, Trans. Amer. Math. Soc. 163 (1972), 207-214. https://doi.org/10.1090/S0002-9947-1972-0290084-3