대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제49권5호
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  • Pages.1041-1055
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  • 2012
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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THE PARAMETER DISTRIBUTION SET FOR A SELF-SIMILAR MEASURE

  • Baek, In-Soo (Department of Mathematics Pusan University of Foreign Studies)
  • 투고 : 2011.06.02
  • 발행 : 2012.09.30
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⟨ 이전 논문 다음 논문 ⟩

초록

The parameter lower (upper) distribution set corresponds to the cylindrical lower or upper local dimension set for a self-similarmeasure on a self-similar set satisfying the open set condition.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea(NRF)

참고문헌

  1. I.-S. Baek, Relation between spectral classes of a self-similar Cantor set, J. Math. Anal. Appl. 292 (2004), no. 1, 294-302. https://doi.org/10.1016/j.jmaa.2003.12.001
  2. I.-S. Baek, Derivative of the Riesz-Nagy -Takacs function, Bull. Korean Math. Soc. 48 (2011), no. 2, 261-275. https://doi.org/10.4134/BKMS.2011.48.2.261
  3. I.-S. Baek, The derivative and moment of the generalized Riesz-Nagy-Takacs function, preprint.
  4. I.-S. Baek, L. Olsen, and N. Snigireva, Divergence points of self-similar measures and packing dimension, Adv. Math. 214 (2007), no. 1, 267-287. https://doi.org/10.1016/j.aim.2007.02.003
  5. R. Cawley and R. D. Mauldin, Multifractal decompositions of Moran fractals, Adv. Math. 92 (1992), no. 2, 196-236. https://doi.org/10.1016/0001-8708(92)90064-R
  6. G. A. Edgar, Measure, Topology, and Fractal Geometry, Springer Verlag, 1990.
  7. M. Elekes, T. Keleti, and A. Mathe, Self-similar and self-affine sets; measures of the intersection of two copies, Ergodic Theory Dynam. Systems 30 (2010), no. 2, 399-440. https://doi.org/10.1017/S0143385709000121
  8. K. J. Falconer, Techniques in Fractal Geometry, John Wiley and Sons, 1997.
  9. W. Li, An equivalent definition of packing dimension and its application, Nonlinear Anal. Real World Appl. 10 (2009), no. 3, 1618-1626. https://doi.org/10.1016/j.nonrwa.2008.02.004
  10. M. Moran, Multifractal components of multiplicative set functions, Math. Nachr. 229 (2001), 129-160. https://doi.org/10.1002/1522-2616(200109)229:1<129::AID-MANA129>3.0.CO;2-L
  11. L. Olsen, A multifractal formalism, Adv. Math. 116 (1995), no. 1, 82-196. https://doi.org/10.1006/aima.1995.1066
  12. L. Olsen and S. Winter, Normal and non-normal points of self-similar sets and divergence points of a self-similar measures, J. London Math. Soc. 67 (2003), no. 3, 103-122. https://doi.org/10.1112/S0024610702003630
  13. A. Schief, Separation properties for self-similar sets, Proc. Amer. Math. Soc. 122 (1994), no. 1, 111-115. https://doi.org/10.1090/S0002-9939-1994-1191872-1

피인용 문헌

  1. THE DIMENSIONS OF THE MINIMUM AND MAXIMUM CYLINDRICAL LOCAL DIMENSION SETS vol.28, pp.1, 2015, https://doi.org/10.14403/jcms.2015.28.1.29
  2. SPECTRAL CLASSES AND THE PARAMETER DISTRIBUTION SET vol.30, pp.3, 2015, https://doi.org/10.4134/CKMS.2015.30.3.221