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Inverse Measures, the Inversion Formula, and Discontinuous Multifractals

โœ Scribed by Benoit B Mandelbrot; Rudolf H Riedi


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
127 KB
Volume
18
Category
Article
ISSN
0196-8858

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๐Ÿ“œ SIMILAR VOLUMES


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โœ Rudolf H Riedi; Benoit B Mandelbrot ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 303 KB

In a previous paper the authors introduced the inverse measure โ€  of a w x probability measure on 0, 1 . It was argued that the respective multifractal โ€  ลฝ . ลฝ . spectra are linked by the ''inversion formula'' f โฃ s โฃ f 1rโฃ . Here, the statements of the previous paper are put into more mathematical t

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## Abstract In this paper, we study the inversion formula for recovering a function from its windowed Fourier transform. We give a rigorous proof for an inversion formula which is known in engineering. We show that the integral involved in the formula is convergent almost everywhere on \documentcla