Czasopismo
Tytuł artykułu
Autorzy
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Języki publikacji
Abstrakty
We investigate the energy of measures (both positive and signed) on compact Riemannian manifolds. A formula is given relating the energy integral of a positive measure with the projections of the measure onto the eigenspaces of the Laplacian. This formula is analogous to the classical formula comparing the energy of a measure in Euclidean space with a weighted L² norm of its Fourier transform. We show that the boundedness of a modified energy integral for signed measures gives bounds on the Hausdorff dimension of the measure. Refined energy integrals and Hausdorff dimensions are also studied and applied to investigate the singularity of Riesz product measures of dimension one.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
291-314
Opis fizyczny
Daty
wydano
2003
Twórcy
autor
- Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
autor
- Department of Mathematics, Chalmers TH & Göteborg University, Eklandagatan 86, SE 412 96, Göteborg, Sweden
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-2-9