Download PDF - Projections of measures with small supportsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Projections of measures with small supports

Authors 1

Affiliations

  1. Analysis, Probability and Fractals Laboratory: LR18ES17, University of Monastir, Department of Mathematics

Abstract

In this paper, we use a characterization of the mutual multifractal Hausdorff dimension in terms of auxiliary measures to investigate the projections of measures with small supports.

Keywords

ENG
Multifractal analysis, Orthogonal projection, s-Ahlfors regular

Bibliography

  1. Attia, Najmeddine, and Bilel Selmi. "Relative multifractal box-dimensions." Filomat 33, no. 9 (2019): 2841-2859.
  2. Attia, Najmeddine, Bilel Selmi, and Chouhaïd Souissi. "Some density results of relative multifractal analysis." Chaos Solitons Fractals 103 (2017): 1-11.
  3. Aouidi, Jamil, and Anouar Ben Mabrouk. "A wavelet multifractal formalism for simultaneous singularities of functions." Int. J. Wavelets Multiresolut. Inf. Process. 12, no. 1 (2014): article no. 1450009.
  4. Barral, Julien, and Imen Bhouri. "Multifractal analysis for projections of Gibbs and related measures." Ergodic Theory Dynam. Systems 31, no. 3 (2011): 673-701.
  5. Cole, Julian David. "Relative multifractal analysis." Chaos Solitons Fractals 11, no. 14 (2000): 2233-2250.
  6. Dai, Meifeng, et al. "Mixed multifractal analysis of crude oil, gold and exchange rate series." Fractals 24, no. 4 (2016): article no. 1650046.
  7. Douzi, Zied, and Bilel Selmi. "Multifractal variation for projections of measures." Chaos Solitons Fractals 91 (2016): 414-420.
  8. Douzi, Zied, and Bilel Selmi. "On the projections of mutual multifractal spectra." Arxiv (2018): arxiv.org/pdf/1805.06866.pdf
  9. Douzi, Zied, and Bilel Selmi. "On the projections of the mutual multifractal Rényi dimensions." Anal. Theory Appl.(to appear).
  10. Falconer, Kenneth John, and John D. Howroyd. "Packing dimensions of projections and dimension profiles." Math. Proc. Cambridge Philos. Soc. 121, no. 2 (1997): 269-286.
  11. Falconer, Kenneth John, and John D. Howroyd. "Projection theorems for box and packing dimensions." Math. Proc. Cambridge Philos. Soc. 119, no. 2 (1996): 287-295.
  12. Falconer, Kenneth John, and Pertti Mattila. "The packing dimension of projections and sections of measures." Math. Proc. Cambridge Philos. Soc. 119, no. 4 (1996): 695-713.
  13. Falconer, Kenneth John, and Toby Christopher O’Neil. "Convolutions and the geometry of multifractal measures." Math. Nachr. 204 (1999): 61-82.
  14. Kaufman, Robert P. "On Hausdorff dimension of projections." Mathematika 15 (1968): 153-155.
  15. Khelifi, Mounir, et al. "A relative multifractal analysis." Chaos Solitons Fractals 140 (2020): article no. 110091.
  16. Marstrand, John Martin "Some fundamental geometrical properties of plane sets of fractional dimensions." Proc. London Math. Soc. (3) 4 (1954): 257-302.
  17. Mattila, Pertti. "Hausdorff dimension, orthogonal projections and intersections with planes." Ann. Acad. Sci. Fenn. Ser. A I Math. 1, no. 2 (1975): 227-244.
  18. Menceur, Mohamed, and Anouar Ben Mabrouk, and Kamel Betina. "The multifractal formalism for measures, review and extension to mixed cases." Anal. Theory Appl. 32, no. 4 (2016): 303-332.
  19. Menceur, Mohamed, and Anouar Ben Mabrouk. "A joint multifractal analysis of vector valued non Gibbs measures." Chaos Solitons Fractals 126 (2019): 203-217.
  20. O’Neil, Toby Christopher. "The multifractal spectra of projected measures in Euclidean spaces." Chaos Solitons Fractals 11, no. 6 (2000): 901-921.
  21. O’Neil, Toby Christopher. "The multifractal spectrum of quasi-self-similar measures." J. Math. Anal. Appl. 211, no. 1 (1997): 233-257.
  22. Olsen, Lars Ole Ronnow. "A multifractal formalism." Adv. Math. 116, no. 1 (1995): 82-196.
  23. Olsen, Lars Ole Ronnow. "Mixed generalized dimensions of self-similar measures." J. Math. Anal. Appl. 306, no. 2 (2005): 516-539.
  24. Rogers, Claude Ambrose. Hausdorff Measures. Cambridge: Cambridge University Press, 1970.
  25. Selmi, Bilel. "A note on the effect of projections on both measures and the generalization of q-dimension capacity." Probl. Anal. Issues Anal. 5(23), no. 2 (2016): 38-51.
  26. Selmi, Bilel. "Measure of relative multifractal exact dimensions." Advances and Applications in Mathematical Sciences 17, no. 10 (2018): 629-643.
  27. Selmi, Bilel. "Multifractal dimensions for projections of measures." Bol. Soc. Paran. Mat. (to appear).
  28. Selmi, Bilel. "On the projections of the multifractal packing dimension for q > 1." Ann. Mat. Pura Appl. (4) 199, no. 4 (2020): 1519-1532.
  29. Selmi, Bilel. "On the strong regularity with the multifractal measures in a probability space." Anal. Math. Phys. 9, no. 3 (2019): 1525-1534.
  30. Selmi, Bilel. "Projection estimates for mutual multifractal dimensions." J. Pure Appl. Math. Adv. 22, no. 1 (2020): 71-89.
  31. Selmi, Bilel. "Appendix to the paper "On the Billingsley dimension of Birkhoff average in the countable symbolic space"." C. R. Math. Acad. Sci. Paris 358, no. 8 (2020): 939.
  32. Selmi, Bilel. "Some new characterizations of Olsen’s multifractal functions." Results Math. 75, no. 4 (2020): paper no. 147.
  33. Selmi, Bilel. "The relative multifractal analysis, review and examples." Acta Sci. Math. (Szeged) 86, no. 3-4 (2020): 635-666.
  34. Selmi, Bilel. "The relative multifractal densities: a review and application." J. Interdiscip. Math. (to appear).
  35. Selmi, Bilel. "On the effect of projections on the Billingsley dimensions." Asian-Eur. J. Math. 13, no. 7 (2020): 2050128.
  36. Selmi, Bilel, and Nina Yuryevna Svetova. "On the projections of mutual Lq,tspectrum." Probl. Anal. Issues Anal. 6(24), no. 2 (2017): 94-108.
  37. Selmi, Bilel, and Nina Yuryevna Svetova. "Projections and Slices of measures." Commun. Korean Math. Soc. (to appear).
  38. Svetova, Nina Yuryevna. "Mutual multifractal spectra. II. Legendre and Hentschel-Procaccia spectra, and spectra defined for partitions." Tr. Petrozavodsk. Gos. Univ. Ser. Mat. 11 (2004): 47-56.
  39. Svetova, Nina Yuryevna. "Mutual multifractal spectra. I. Exact spectra." Tr. Petrozavodsk. Gos. Univ. Ser. Mat. 11 (2004): 41-46.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
2021/20
Export to PBN, Opens in new tab
Pages:
5-15
Main language of publication
English
Published
2021-02-01