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Convolutions and the Geometry of Multifractal Measures

โœ Scribed by K. J. Falconer; T. C. O'Neil

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
936 KB
Volume
204
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

Abrtrrct. This paper relates multifractd featurea of a measure p on IR" to thoee of the projection of the measure onto m-dimensional subpaces. We .chieve thin through the rtudy of appropriately defined convolution kern&. This provides a unified approrcb to projections of measurea and leads to new reaults on multifirctal properties m d l aa rltemative denntiona of some exbting formulae. These include formulae and estimates tor the l d dimedonr and generlioed p-dimenr~ons of projected measurea M well aa more precise information about the limiting behaviour of multifwtal exprenaionr. We consider briatly how rimilu idem may be applied to rsetiona of a memure by (nm)dimendond p h e a .

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