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Fourier-Feynman transforms of unbounded functionals on abstract Wiener space

Byoung Kim, Il Yoo, Dong Cho (2010)

Open Mathematics

Huffman, Park and Skoug established several results involving Fourier-Feynman transform and convolution for functionals in a Banach algebra S on the classical Wiener space. Chang, Kim and Yoo extended these results to abstract Wiener space for a more generalized Fresnel class ℱ 𝒜 1 , 𝒜 2 A1,A2 than the Fresnel class ℱ (B)which corresponds to the Banach algebra S. In this paper we study Fourier-Feynman transform, convolution and first variation of unbounded functionals on abstract Wiener space having the form...

Fractal negations.

Gaspar Mayor Forteza, Tomasa Calvo Sánchez (1994)

Mathware and Soft Computing

From the concept of attractor of a family of contractive affine transformations in the Euclidean plane R2, we study the fractality property of the De Rham function and other singular functions wich derive from it. In particular, we show as fractals the strong negations called k-negations.

Fractal star bodies

Irmina Herburt, Maria Moszyńska, Dorette Pronk (2009)

Banach Center Publications

In 1989 R. Arnold proved that for every pair (A,B) of compact convex subsets of ℝ there is an Euclidean isometry optimal with respect to L₂ metric and if f₀ is such an isometry, then the Steiner points of f₀(A) and B coincide. In the present paper we solve related problems for metrics topologically equivalent to the Hausdorff metric, in particular for L p metrics for all p ≥ 2 and the symmetric difference metric.

Fractal-classic interpolants

M. A. Navascués, M. V. Sebastián (2009)

Banach Center Publications

The methodology of fractal interpolation is very useful for processing experimental signals in order to extract their characteristics of complexity. We go further and prove that the Iterated Function System involved may also be used to obtain new approximants that are close to classical ones. In this work a classical function and a fractal function are combined to construct a new interpolant. The fractal function is first defined as a perturbation of a classical mapping. The additional condition...

Fractional multiplicative processes

Julien Barral, Benoît Mandelbrot (2009)

Annales de l'I.H.P. Probabilités et statistiques

Statistically self-similar measures on [0, 1] are limit of multiplicative cascades of random weights distributed on the b-adic subintervals of [0, 1]. These weights are i.i.d., positive, and of expectation 1/b. We extend these cascades naturally by allowing the random weights to take negative values. This yields martingales taking values in the space of continuous functions on [0, 1]. Specifically, we consider for each H∈(0, 1) the martingale (Bn)n≥1 obtained when the weights take the values −b−H...

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