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[56] Random coverings in several dimensions

Svante Janson Uppsala University, Uppsala, Sweden

TBD mathscidoc:1701.331673

Acta Mathematica, 156, (1), 83-118, 1983.10

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Bock H. Probabilistic models in cluster analysis[J]. Computational Statistics \u0026 Data Analysis, 1996, 23(1): 5-28.

Wang H, Xia Y. Shrinkage Estimation of the Varying Coefficient Model[J]. Journal of the American Statistical Association, 2008, 104(486): 747-757.

Cuevas A, Fraiman R. A plug-in approach to support estimation[J]. Annals of Statistics, 1997, 25(6): 2300-2312.

Illo A B, Cuevas A, Justel A, et al. Set estimation and nonparametric detection[J]. Canadian Journal of Statistics-revue Canadienne De Statistique, 2000, 28(4): 765-782.

Cuevas A, Rodriguezcasal A. On boundary estimation[J]. Advances in Applied Probability, 2004, 36(2): 340-354.

Deheubvels P, Einmahl J H, Mason D M, et al. The almost sure behavior of maximal and minimal multivariate k n -spacings[J]. Journal of Multivariate Analysis, 1988, 24(1): 155-176.

Cuevas A, Fraiman R, Rodriguezcasal A, et al. A Nonparametric Approach to the Estimation of Lengths and Surface Areas[J]. Annals of Statistics, 2007, 35(3): 1031-1051.

Mladen Kolar · Ankur P Parikh · Eric P Xing. On Sparse Nonparametric Conditional Covariance Selection. 2010.

Zhao W, Zhang R, Lv Y, et al. Variable selection of the quantile varying coefficient regression models[J]. Journal of The Korean Statistical Society, 2013, 42(3): 343-358.

Berrendero J R, Cuevas A, Vjosazquezgrande F, et al. Testing multivariate uniformity: the distance-to-boundary method[J]. Canadian Journal of Statistics-revue Canadienne De Statistique, 2006, 34(4): 693-707.

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[57] On a special class of$p$-groups

N. Blackburn Manchester, England

TBD mathscidoc:1701.331154

Acta Mathematica, 100, (1), 45-92, 1958.3

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Besche H U, Eick B, Obrien E A, et al. A MILLENNIUM PROJECT: CONSTRUCTING SMALL GROUPS[J]. International Journal of Algebra and Computation, 2011, 12(05): 623-644.

Leedhamgreen C R, Newman M. Space groups and groups of prime-power order I[J]. Archiv der Mathematik, 1980, 35(1): 193-202.

Suzuki M. On a finite group with a partition[J]. Archiv der Mathematik, 1961, 12(1): 241-254.

Obrien E A, Vaughanlee M R. The groups with order p7 for odd prime p[J]. Journal of Algebra, 2005, 292(1): 243-258.

Aner Shalev. The structure of finite p-groups: effective proof of the coclass conjectures. 1994.

Alperin J L. AUTOMORPHISMS OF SOLVABLE GROUPS[J]. Proceedings of the American Mathematical Society, 1962, 13(2): 175-180.

Walter J H. Finite groups with abelian sylow 2-subgroups of order 8[J]. Inventiones Mathematicae, 1967, 2(5): 332-376.

Guy T Hogan · Wolfgang P Kappe. On the _{}-problem for finite -groups. 1969.

Newman M, Obrien E A, Vaughanlee M R, et al. Groups and nilpotent Lie rings whose order is the sixth power of a prime[J]. Journal of Algebra, 2004, 278(1): 383-401.

Obrien E A, Vaughanlee M R. The groups with order p 7 for odd prime p[J]. Journal of Algebra, 2005, 292(1): 243-258.

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[58] Regular iteration of real and complex functions

G. Szekeres University of Adelaide, South Australia

TBD mathscidoc:1701.331158

Acta Mathematica, 100, (3), 203-258, 1958.9

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Odlyzko A. Asymptotic enumeration methods[C]., 1996: 1063-1229.

Cowen C C. Iteration and the solution of functional equations for functions analytic in the unit disk[J]. Transactions of the American Mathematical Society, 1981, 265(1): 69-95.

Renyi A, Szekeres G. On the height of trees[J]. Journal of The Australian Mathematical Society, 1967, 7(04): 497-507.

Seneta E. Functional equations and the Galton-Watson process[J]. Advances in Applied Probability, 1969, 1(01): 1-42.

Bingham N H, Divisibility I. On the Limit of a Supercritical Branching Process[J]. Journal of Applied Probability, 2016: 215-228.

Karlin S, Mcgregor J. Embeddability of discrete time simple branching processes into continuous time branching processes[J]. Transactions of the American Mathematical Society, 1968, 132(1): 115-136.

Baker I N. Permutable power series and regular iteration[J]. Journal of The Australian Mathematical Society, 1962, 2(03): 265-294.

Karlin S, Mcgregor J. Embedding iterates of analytic functions with two fixed points into continuous groups[J]. Transactions of the American Mathematical Society, 1968, 132(1): 137-145.

Flajolet P, Gao Z, Odlyzko A, et al. The Distribution of Heights of Binary Trees and Other Simple Trees[J]. Combinatorics, Probability \u0026 Computing, 1993, 2(02): 145-156.

Pittel B. On growing random binary trees[J]. Journal of Mathematical Analysis and Applications, 1984, 103(2): 461-480.

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[59] A proof of Furstenberg’s conjecture on the intersections of ×𝑝- and ×𝑞-invariant sets

Meng Wu Department of Mathematical Sciences, University of Oulu, Oulu, Finland

TBD mathscidoc:2203.43023

Annals of Mathematics, 189, 707-751, 2019.5

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We prove the following conjecture of Furstenberg (1969): if 𝐴,𝐵⊂[0,1] are closed and invariant under ×𝑝 mod1 and ×𝑞 mod1, respectively, and if log𝑝/log𝑞∉ℚ, then for all real numbers 𝑢 and 𝑣, dim_H (𝑢𝐴 + 𝑣) ∩ 𝐵 ≤ max {0, dim_H 𝐴 + dim_H 𝐵 − 1}. We obtain this result as a consequence of our study on the intersections of incommensurable self-similar sets on ℝ. Our methods also allow us to give upper bounds for dimensions of arbitrary slices of planar self-similar sets satisfying SSC and certain natural irreducible conditions.

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[60] On the existence of certain singular integrals

A. P. Calderon A. Zygmund

TBD mathscidoc:1701.331054

Acta Mathematica, 88, (1), 85-139, 1952.12

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Agmon S, Douglis A, Nirenberg L, et al. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I[J]. Communications on Pure and Applied Mathematics, 1959, 12(4): 623-727.

Fefferman C, Stein E M. H p spaces of several variables[J]. Acta Mathematica, 1972, 129(1): 137-193.

Coifman R R, Weiss G. Extensions of Hardy spaces and their use in analysis[J]. Bulletin of the American Mathematical Society, 1977, 83(4): 569-645.

Lars Hormander. Estimates for translation invariant operators inL p spaces. 1960.

Brudnyi Y A, Krein S G, Semenov E M, et al. Interpolation of linear operators[J]. Journal of Mathematical Sciences, 1988, 42(6): 2009-2113.

Zygmund A. On singular integrals[J]. American Journal of Mathematics, 2011, 78(2): 68-105.

Lars V Ahlfors · Lipman Bers. RIEMANN'S MAPPING THEOREM FOR VARIABLE METRICS*. 1960.

Baratchart L, Leblond J, Rigat S, et al. Hardy spaces of the conjugate Beltrami equation[J]. Journal of Functional Analysis, 2009, 259(2): 384-427.

Stein E M, Wainger S. Problems in harmonic analysis related to curvature[J]. Bulletin of the American Mathematical Society, 1978, 84(6): 1239-1295.

Kalaj D. On the Nitsche conjecture for harmonic mappings in ℝ2 and ℝ3[J]. Israel Journal of Mathematics, 2005, 150(1): 241-251.

[ Cited by 452 ]

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TBD

[56] Random coverings in several dimensions

Svante Janson Uppsala University, Uppsala, Sweden

TBD mathscidoc:1701.331673

[57] On a special class of$p$-groups

N. Blackburn Manchester, England

TBD mathscidoc:1701.331154

[58] Regular iteration of real and complex functions

G. Szekeres University of Adelaide, South Australia

TBD mathscidoc:1701.331158

[59] A proof of Furstenberg’s conjecture on the intersections of ×𝑝- and ×𝑞-invariant sets

Meng Wu Department of Mathematical Sciences, University of Oulu, Oulu, Finland

TBD mathscidoc:2203.43023

[60] On the existence of certain singular integrals

A. P. Calderon A. Zygmund

TBD mathscidoc:1701.331054

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