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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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Contents: J. C. R. Hunt, N. K.-R. Kevlahan, J. C. Vassilicos and M. Farge, Wavelets, fractals and Fourier transforms: detection and analysis of structure (1–38); K. J. Falconer, Wavelets, fractals and order-two densities (39–46); S. Jaffard, Orthonormal and continuous wavelet transform: algorithms and applications to the study of pointwise properties of functions (47–64); J. Stark and P. Bressloff, Iterated function systems and their applications (65–90); C. Herley and M. Vetterli, Biorthogonal bases of symmetric compactly supported wavelets (91–108);
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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