DOI QR코드

DOI QR Code

SETS OF UNIQUENESS, WEAKLY SUFFICIENT SETS AND SAMPLING SETS FOR A-∞(B)

  • Khoi, Le Hai
  • Received : 2009.03.05
  • Accepted : 2010.07.12
  • Published : 2010.09.30

Abstract

We study a relationship between sets of uniqueness, weakly sufficient sets and sampling sets in the space $A^{-{\infty}}(\mathbb{B})$ of holomorphic functions with polynomial growth on the unit ball of $\mathbb{C}^n$ ($n\;{\geq}\;1$).

Keywords

sampling set;weakly sufficient set;set of uniqueness;function algebra;polynomial growth

References

  1. A. V. Abanin, Some criteria for weak sufficiency, Mat. Zametki 40 (1986), no. 4, 442-454
  2. A. V. Abanin, Some criteria for weak sufficiency, Math. Notes 40 (1986), no. 3-4, 757-764. https://doi.org/10.1007/BF01159666
  3. 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
  4. Y. J. Choi, L. H. Khoi, and K. T. Kim, On an explicit construction of weakly sufficient sets for the function algebra $A^{-{\infty}}({\Omega})$, Complex Var. Elliptic Equ. 54 (2009), no. 9, 879-897. https://doi.org/10.1080/17476930903030028
  5. C. A. 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
  6. V. Ganapathy Iyer, On effective sets of points in relation to integral functions, Trans. Amer. Math. Soc. 42 (1937), no. 3, 358-365 https://doi.org/10.1090/S0002-9947-1937-1501926-4
  7. V. Ganapathy Iyer, On effective sets of points in relation to integral functions, Trans. Amer. Math. Soc. 43 (1938), no. 3, 494.
  8. L. H. Khoi and P. J. Thomas, Weakly sufficient sets for $A^{-{\infty}}$(D), Publ. Mat. 42 (1998), no. 2, 435-448. https://doi.org/10.5565/PUBLMAT_42298_10
  9. H. Komatsu, Projective and injective limits of weakly compact sequences of locally convex spaces, J. Math. Soc. Japan 19 (1967), 366-383. https://doi.org/10.2969/jmsj/01930366
  10. X. Massaneda, Interpolation by holomorphic functions in the unit ball with polynomial growth, Ann. Fac. Sci. Toulouse Math. (6) 6 (1997), no. 2, 277-296. https://doi.org/10.5802/afst.866
  11. X. Massaneda, $A^{-{\infty}}$-interpolation in the ball, Proc. Edinburgh Math. Soc. (2) 41 (1998), no. 2, 359-367. https://doi.org/10.1017/S0013091500019702
  12. 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.

Cited by

  1. Cauchy–Fantappiè transformation and mutual dualities between and for lineally convex domains vol.349, pp.21-22, 2011, https://doi.org/10.1016/j.crma.2011.10.013
  2. Mutual dualities betweenA−∞(Ω) and for lineally convex domains vol.58, pp.11, 2013, https://doi.org/10.1080/17476933.2012.699963
  3. Effective and Sampling Sets for Hörmander Spaces 2016, https://doi.org/10.1007/s11785-016-0560-5