Zobrazeno 1 - 10
of 102
pro vyhledávání: '"Pertti Mattila"'
Autor:
Pertti Mattila
Publikováno v:
Mathematical and Computational Applications, Vol 28, Iss 2, p 49 (2023)
Let A and B be Borel subsets of the Euclidean n-space with dimA+dimB>n. This is a survey on the following question: what can we say about the Hausdorff dimension of the intersections A∩(g(B)+z) for generic orthogonal transformations g and translati
Externí odkaz:
https://doaj.org/article/62688c9218d24ba4a53b73e5eaa67928
Autor:
Pertti Mattila
Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, includ
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5b3a5e8be6e8c91b9b785da038e5a79f
https://doi.org/10.1017/9781009288057
https://doi.org/10.1017/9781009288057
Autor:
Pertti Mattila
Publikováno v:
Trends in Mathematics ISBN: 9783030744168
Trends in Mathematics
Trends in Mathematics
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cce422caa9a2a50e29aeea245341baee
https://doi.org/10.1007/978-3-030-74417-5_19
https://doi.org/10.1007/978-3-030-74417-5_19
Autor:
Pertti Mattila
Publikováno v:
Recercat. Dipósit de la Recerca de Catalunya
instname
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Publicacions Matemàtiques; Vol. 40, Núm. 1 (1996); p. 195-204
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Publicacions Matemàtiques; Vol. 40, Núm. 1 (1996); p. 195-204
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
We show that if a Cantor set $E$ as considered by Garnett in \cite{G2} has positive Hausdorff $h$-measure for a non-decreasing function $h$ satisfying $\int^1_0r^{-3}\,h(r)^2\,dr < \infty$, then the analytic capacity of $E$ is positive. Our tool will
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7517d99328b42194a2005ba3ee317a1f
http://hdl.handle.net/2072/391773
http://hdl.handle.net/2072/391773
Autor:
Pertti Mattila
Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, includ
Autor:
Pertti Mattila
Publikováno v:
New Trends in Applied Harmonic Analysis, Volume 2 ISBN: 9783030323523
This is a survey on recent developments on the Hausdorff dimension of projections and intersections for general subsets of Euclidean spaces, with an emphasis on estimates of the Hausdorff dimension of exceptional sets and on restricted projection fam
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::06bfa5e934d4acdf4c2bad8f60169e7d
https://doi.org/10.1007/978-3-030-32353-0_6
https://doi.org/10.1007/978-3-030-32353-0_6
Autor:
Kenneth J. Falconer, Pertti Mattila
Publikováno v:
Journal of Fractal Geometry. 3:319-329
We present strong versions of Marstrand's projection theorems and other related theorems. For example, if E is a plane set of positive and finite s-dimensional Hausdorff measure, there is a set X of directions of Lebesgue measure 0, such that the pro
Autor:
Pertti Mattila
Let A and B be Borel subsets of the Euclidean n-space with dim A + dim B > n and let 0 u for z in a set of positive Lebesgue measure. If dim A + dim B
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4cd8d59a40085a3b5039af355e03fa56
http://hdl.handle.net/10138/224529
http://hdl.handle.net/10138/224529
Autor:
Estibalitz Durand-Cartagena, Zoltán M. Balogh, Jeremy T. Tyson, Katrin Fässler, Pertti Mattila
Publikováno v:
Rev. Mat. Iberoam.
We prove analogs of classical almost sure dimension theorems for Euclidean projection mappings in the first Heisenberg group, equipped with a sub-Riemannian metric.
Autor:
Vasileios Chousionis, Pertti Mattila
Publikováno v:
Journal für die reine und angewandte Mathematik (Crelles Journal). 2014:29-60
In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean spaces and Heisenberg groups. In addition to obtaining