On the projections of mutual $L^{q,t}$-spectrum
Problemy analiza, Tome 6 (2017) no. 2, pp. 94-108.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we are interested in the mutual $L^{q,t}$-spectrum relatively to two Borel probability measures having the same compact support and also in the study of their behavior under orthogonal projections.
Keywords: mutual multifractal analysis.
Mots-clés : orthogonal projection, dimension spectra
@article{PA_2017_6_2_a5,
     author = {B. Selmi and N. Yu. Svetova},
     title = {On the projections of mutual $L^{q,t}$-spectrum},
     journal = {Problemy analiza},
     pages = {94--108},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2017_6_2_a5/}
}
TY  - JOUR
AU  - B. Selmi
AU  - N. Yu. Svetova
TI  - On the projections of mutual $L^{q,t}$-spectrum
JO  - Problemy analiza
PY  - 2017
SP  - 94
EP  - 108
VL  - 6
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2017_6_2_a5/
LA  - en
ID  - PA_2017_6_2_a5
ER  - 
%0 Journal Article
%A B. Selmi
%A N. Yu. Svetova
%T On the projections of mutual $L^{q,t}$-spectrum
%J Problemy analiza
%D 2017
%P 94-108
%V 6
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2017_6_2_a5/
%G en
%F PA_2017_6_2_a5
B. Selmi; N. Yu. Svetova. On the projections of mutual $L^{q,t}$-spectrum. Problemy analiza, Tome 6 (2017) no. 2, pp. 94-108. http://geodesic.mathdoc.fr/item/PA_2017_6_2_a5/

[1] Bahroun F., Bhouri I., “Multifractals and projections”, Extracta Mathematicae, 21 (2006), 83–91 | MR | Zbl

[2] Barral J., Bhouri I., “Multifractal analysis for projections of Gibbs and related measures”, Ergodic Theory and Dynamic systems, 31 (2011), 673–701 | DOI | MR | Zbl

[3] Bhouri I., “On the projections of generalized upper $L^q$-spectrum”, Chaos, Solitons and Fractals, 42 (2009), 1451–1462 | DOI | MR | Zbl

[4] Douzi Z., Selmi B., “Multifractal variation for projections of measures”, Chaos, Solitons and Fractals, 91 (2016), 414–420 | DOI | MR | Zbl

[5] Douzi Z., Selmi B., On the projections of mutual multifractal spectra, Preprint, 2017

[6] Douzi Z., Selmi B., On the projections of the mutual multifractal Réyni dimensions, Preprint, 2017

[7] Falconer K. J., Howroyd J. D., “Packing Dimensions of Projections and Dimensions Profiles”, Math. Proc. Cambridge Philos. Soc., 121 (1997), 269–286 | DOI | MR | Zbl

[8] Falconer K. J., Mattila P., “The Packing Dimensions of Projections and Sections of Measures”, Math. Proc. Cambridge Philos. Soc., 119:4 (1996), 695–713 | DOI | MR | Zbl

[9] Falconer K. J., Mattila P., “The Packing Dimensions of Projections and Sections of Measures”, Math. Proc. Cambridge Philos. Soc., 119:4 (1996), 695–713 | DOI | MR | Zbl

[10] Hu X., Taylor J., “Fractal properties of products and projections of measures in $\mathbb{R}^n$”, Math. Proc. Cambridge Philos. Soc., 115:3 (1994), 527–544 | DOI | MR | Zbl

[11] Hunt B. R., Kaloshin V. Y., “How projections affect the dimension spectrum of fractal measures”, Nonlinearity, 10 (1997), 1031–1046 | DOI | MR | Zbl

[12] Järvenpää E., Järvenpä M., Ledrappier F., Leikas M., “One-dimensional families of projections”, Nonlinearity, 21 (2008), 453–464 | DOI | MR

[13] Järvenpä E., Järvenpä M., Keleti T., “Hausdorff Dimension and Nondegenerate Families of Projections”, The Journal of Geometric Analysis, 24:4 (2014), 2020–2034 | DOI | MR | Zbl

[14] Kaufman R., “On Hausdorff dimension of projections”, Mathematika, 15 (1968), 153–155 | DOI | MR | Zbl

[15] Marstrand J. M., “Some fundamental geometrical properties of plane sets of fractional dimensions”, Proceedings of the London Mathematical Society, 4 (1954), 257–302 | DOI | MR | Zbl

[16] Mattila P., “Hausdorff dimension, orthogonal projections and intersections with planes”, Annales Academiae Scientiarum Fennicae. Series A Mathematica, 1 (1975), 227–244 | DOI | MR | Zbl

[17] Mattila P., The Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, Cambrdige, 1995 | DOI | MR

[18] Olsen L., “Mixed generalized dimensions of self-similar measures”, Journal of Mathematical Analysis and Applications, 306:2 (2005), 516–539 | DOI | MR | Zbl

[19] O'Neil T. C., “The multifractal spectra of projected measures in Euclidean spaces”, Chaos, Solitons and Fractals, 11 (2000), 901–921 | DOI | MR | Zbl

[20] Selmi B., “A note on the effect of projections on both measures and the generalization of $q$-dimension capacity”, Probl. Anal. Issues Anal., 5 (2016), 38–51 | DOI | MR | Zbl

[21] Selmi B., Multifractal dimensions for projections of measures, Preprint, 2017

[22] Svetova N. Yu., “Mutual multifractal spectra II: Legendre and Hentschel-Procaccia spectra, and spectra defined for partitions”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 11 (2004), 47–56 | MR

[23] Svetova N. Yu., “Numerical algorithm of the mutual multifractal analysis”, Electronic Journal "Investigated in Russia", 2004, 1971–1980

[24] Svetova N. Yu., “The property of convexity of mutual multifractal dimension”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 17 (2010), 15–24 | MR

[25] Svetova N. Yu., “Mutual multifractal spectra I: Exact spectra”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 11 (2004), 41–46 | MR | Zbl

[26] Svetova N. Yu., “An estimate for exact mutual multifractal spectra”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 14 (2008), 59–66 | MR

[27] Svetova N. Yu., “The relative Renyi dimension”, Probl. Anal. Issues Anal., 1 (2012), 15–23 | DOI | MR | Zbl