Energy of measures on compact Riemannian manifolds

• Autorzy: Kathryn E. Hare , Maria Roginskaya
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42A55: Lacunary series of trigonometric and other functions; Riesz products
• 58C35: Integration on manifolds; measures on manifolds
• 28A12: Contents, measures, outer measures, capacities
• 28A78: Hausdorff and packing measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 159
• Numer: 2
• Strony: 291-314

Daty

wydano

2003

Twórcy

autor

Kathryn E. Hare

• Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

autor

Maria Roginskaya

• Department of Mathematics, Chalmers TH & Göteborg University, Eklandagatan 86, SE 412 96, Göteborg, Sweden

Identyfikatory

DOI

10.4064/sm159-2-9