Wavelets, fractals, and Fourier transforms. Based on the proceedings of a conference, organized by the Institute of Mathematics and its Applications and Société de Mathématiques Appliquées et Industrielles and held at Newnham College, Cambridge, UK, in December 1990.

*(English)*Zbl 0809.00021
The Institute of Mathematics and Its Applications Conference Series. New Series. 43. Oxford: Clarendon Press. xv, 403 p. (1993).

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P. Flandrin, Fractional Brownian motion and wavelets (109–122); H. O. Rasmussen, The wavelet Gibbs phenomenon (123–142); P. L. Vermeer and J. A. H. Alkemade, Multiscale segmentation of well logs (143–149); D. J. Field, Scale-invariance and self-similar “wavelet” transforms: an analysis of natural scenes and mammalian visual systems (151–193); A. Bijaoui, Wavelets and astronomical image analysis (195–212);

A. Bijaoui, E. Slezak and G. Mars, Universe heterogeneities from a wavelet analysis (213–220); B. Sinha and K. J. Richards, The wavelet transform applied to flow around Antarctica (221–228); P. H. Haynes and W. A. Norton, Quantification of scale cascades in the stratosphere using wavelet transforms (229–234); J. G. Jones, P. G. Earwicker and G. W. Foster, Multiple-scale correlation detection, wavelet transforms and multifractal turbulence (235–250); C. Meneveau, Wavelet analysis of turbulence: the mixed energy cascade (251–264); P. Frick and V. Zimin, Hierarchical models of turbulence (265–283); M. Luoni, Characterisation of ATM traffic in the frequency domain (285–294); S. N. Gurbatov and A. I. Saichev, The self-similarity of \(d\)-dimensional potential turbulence (295–307);

J. Caldwell, Solution of Burgers’ equation by Fourier transform methods (309–315); H. K. Moffatt, Spiral structures in turbulent flow (317–324); J. C. Vassilicos, Fractals in turbulence (325–340); A. Malakhov and A. Yakimov, The physical models and mathematical description of \(1/f\) noise (341–352); J. M. Redondo, Fractal models of density interfaces (353–370); G. Sæther, K. Bendiksen, J. Muller and E. Frøland, The fractal dimension of oil-water interfaces in channel flows (371–378); J. M. Redondo, R. M. Gonzalez and J. L. Cano, Fractal aggregates in the atmosphere (379–396); J. Muller, Morphology of disordered materials studied by multifractal analysis (397–403).

The articles of this volume will be reviewed individually.

Indexed articles:

Hunt, J. C. R.; Kevlahan, N. K.-R.; Vassilicos, J. C.; Farge, M., Wavelets, fractals and Fourier transforms: Detection and analysis of structure, 1-38 [Zbl 0978.42504]

Falconer, K. J., Wavelets, fractals and order-two densities, 39-46 [Zbl 0829.28004]

Jaffard, S., Orthonormal and continuous wavelet transform: Algorithms and applications to the study of pointwise properties of functions, 47-64 [Zbl 0838.42017]

Stark, J.; Bressloff, P., Iterated function systems and their applications, 65-90 [Zbl 0827.28006]

Herley, C.; Vetterli, M., Biorthogonal bases of symmetric compactly supported wavelets, 91-108 [Zbl 0813.42023]

Flandrin, P., Fractional Brownian motion and wavelets, 109-122 [Zbl 0826.60032]

Rasmussen, H. O., The wavelet Gibbs phenomenon, 123-142 [Zbl 0813.42019]

Vermeer, P. L.; Alkemade, J. A. H., Multiscale segmentation of well logs, 143-149 [Zbl 1107.94325]

Field, D. J., Scale-invariance and self-similar ‘wavelet’ transforms: An analysis of natural scenes and mammalian visual systems, 151-193 [Zbl 0818.42013]

Bijaoui, A., Wavelets and astronomical image analysis, 195-212 [Zbl 0925.42015]

Bijaoui, A.; Slezak, E.; Mars, G., Universe heterogeneities from a wavelet analysis, 213-220 [Zbl 0850.42002]

Sinha, B.; Richards, K. J., The wavelet transform applied to flow around Antarctica, 221-228 [Zbl 0825.76029]

Haynes, P. H.; Norton, W. A., Quantification of scale cascades in the stratosphere using wavelet transforms, 229-234 [Zbl 0825.76028]

Jones, J. G.; Earwicker, P. G.; Foster, G. W., Multiple-scale correlation detection, wavelet transforms and multifractal turbulence, 235-250 [Zbl 0813.42024]

Meneveau, C., Wavelet analysis of turbulence: The mixed energy cascade, 251-264 [Zbl 0817.76022]

Frick, P.; Zimin, V., Hierarchical models of turbulence, 265-283 [Zbl 0821.76036]

Luoni, M., Characterisation of ATM traffic in the frequency domain, 285-294 [Zbl 0819.94003]

Gurbatov, S. N.; Saichev, A. I., The self-similarity of \(D\)-dimensional potential turbulence, 295-307 [Zbl 0817.76024]

Caldwell, J., Solution of Burgers’ equation by Fourier transform methods, 309-315 [Zbl 0816.65066]

Moffatt, H. K., Spiral structures in turbulent flow, 317-324 [Zbl 0824.76034]

Vassilicos, J. C., Fractals in turbulence, 325-340 [Zbl 0817.76026]

Malakhov, A.; Yakimov, A., The physical models and mathematical description of 1/fnoise, 341-352 [Zbl 0825.00026]

Redondo, J. M., Fractal models of density interfaces, 353-370 [Zbl 0817.76025]

Sæther, G.; Bendiksen, K.; Muller, J.; Frøland, E., The fractal dimension of oil-water interfaces in channel flows, 371-378 [Zbl 0825.76874]

Redondo, J. M.; Gonzalez, R. M.; Cano, J. L., Fractal aggregates in the atmosphere, 379-396 [Zbl 0825.76873]

Muller, J., Morphology of disordered materials studied by multifractal analysis, 397-403 [Zbl 0825.28007]

##### MSC:

00B25 | Proceedings of conferences of miscellaneous specific interest |

42-06 | Proceedings, conferences, collections, etc. pertaining to harmonic analysis on Euclidean spaces |

42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |

28A80 | Fractals |

42A16 | Fourier coefficients, Fourier series of functions with special properties, special Fourier series |

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\textit{M. Farge} (ed.) et al., Wavelets, fractals, and Fourier transforms. Based on the proceedings of a conference, organized by the Institute of Mathematics and its Applications and Société de Mathématiques Appliquées et Industrielles and held at Newnham College, Cambridge, UK, in December 1990. Oxford: Clarendon Press (1993; Zbl 0809.00021)