Functions and Analysis

1804 Submissions

[2] viXra:1804.0405 [pdf] submitted on 2018-04-26 11:14:24

Mixed Generalized Multifractal Densities for Vector Valued Quasi-Ahlfors Measures

Authors: Adel Farhat, Anouar Ben Mabrouk
Comments: 19 Pages.

In the present work we are concerned with some density estimations of vector valued measures in the framework of the so-called mixed multifractal analysis. We precisely consider some Borel probability measures satisfying a weak quasi-Alfors regularity. Mixed multifractal generalizations of densities are then introduced and studied in a framework of relative mixed multifractal analysis.
Category: Functions and Analysis

[1] viXra:1804.0264 [pdf] replaced on 2018-04-23 04:22:49

On Expanding a Function Into Raw Moment Series

Authors: Andrej Liptaj
Comments: 10 Pages.

I focus in this text on the construction of functions f_{j} with the delta property C_{i}\left(f_{j}\right)=\delta_{i,j}, where C_{i} are operators which associate to a function its i-th raw moment. A formal method for their construction is found, however results are divergent, from what a non-existence of such functions is conjectured. This also prevents an elegant series expansion with order-by-order moment matching. For a finite interval some partial results are presented: a method of expansion into raw moment series for finite number of moments and a “non-delta” method based on computing Legendre-expansion coefficients from moments (an already known method [1]). As by-product some coefficients formulas are found: coefficients for expanding a Hermite function into the Taylor series and coefficients for expanding into the Taylor series an element of a Fourier series (i.e. common formula for sine and cosine) thus formally merging the two (sine and cosine) Fourier sub-series into one.
Category: Functions and Analysis