Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Cover of the book

2017 | OriginalPaper | Chapter

New Exponents for Pointwise Singularity Classification

Authors : Patrice Abry, Stéphane Jaffard, Roberto Leonarduzzi, Clothilde Melot, Herwig Wendt

Published in: Recent Developments in Fractals and Related Fields

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We introduce new tools for pointwise singularity classification: We investigate the properties of the two-variable function which is defined at every point as the p-exponent of a fractional integral of order t; new exponents are derived which are not of regularity type but give a more precise description of the behavior of the function near a singularity. We revisit several classical examples (deterministic and random) of multifractal functions for which the additional information supplied by this classification is derived. Finally, a new example of multifractal function is studied, where these exponents prove pertinent.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
next chapter The Two-Dimensional Density of Bernoulli Convolutions
Appendix
Available only for authorised users
Literature
1.
Abry, P., Jaffard, S., Roux, S.G.: In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Praha (2011)
2.
3.
4.
5.
Barral, J., Mandelbrot, B.: In: Lapidus, M.L., van Frankenhuysen, M. (eds.) Proc. Symp. Pures Math., vol. 72, p. 1 (2004)
6.
Calderon, A.P., Zygmund, A.: Stud. Math. 20, 171 (1961)
7.
Jaffard, S.: C.R.A.S., Série 1 315, 19 (1992)
8.
9.
10.
11.
Jaffard, S.: Fractal Geometry and Applications: A Jubilee of Benoît Mandelbrot, In: Lapidus, M., van Frankenhuijsen, M. (eds.) Proceedings of the Symposia in Pure Mathematics, vol. 72(2), pp. 91–152. AMS, Providence (2004)
12.
Jaffard, S.: In: Figiel, T., Kamont, A. (eds.) Approximation and Probability, vol. 72, pp. 93–110. Banach Center Pub., Warsaw (2006)
13.
Jaffard, S., Meyer, Y.: Wavelet methods for pointwise regularity and local oscillations of functions. Mem. Am. Math. Soc. 123 (1996)
14.
15.
Jaffard, S., Melot, C.: Commun. Math. Phys. 258(3), 513 (2005). doi:10.1007/s00220-005-1354-1CrossRef
16.
Jaffard, S., Abry, P., Roux, S.G.: In: Bergounioux, M. (ed.) Mathematical Image Processing. Springer Proceedings in Mathematics, vol. 5, p. 1. Springer-Verlag Berlin Heidelberg (2011)
17.
Jaffard, S., Abry, P., Melot, C., Leonarduzzi, R., Wendt, H.: In: Bandt, C., et al. (eds.) Fractal Geometry and Stochastics V. Series Progress in Probability, vol. 70, p. 279. Birkhäuser, Boston (2015)
18.
19.
Leonarduzzi, R., Spika, J., Wendt, H., Jaffard, S., Torres, M.E., Abry, P., Doret, M.: In: Proceedings of the Latin American Conference on Biomedical Engineering (CLAIB). Paraná, Entre Ríos, Argentina, October 2014
20.
Leonarduzzi, R., Spilka, J., Frecon, J., Wendt, H., Pustelnik, N., Jaffard, S., Abry, P., Doret, M.: In: Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 1971–1974. IEEE, New York (2015)
21.
22.
23.
Meyer, Y.: Ondelettes et Opérateurs. Hermann, Paris (1990). English translation, Wavelets and Operators. Cambridge University Press, Cambridge (1992)
24.
25.
26.
Parisi, G., Frisch, U.: Turbulence and predictability in geophysical fluid dynamics and climate dynamics. In: Ghil, M., Benzi, R., Parisi, G. (eds.) Proceedings of the International School, p. 84. North-Holland, Amsterdam (1985)
27.
Seuret, S., Ubis, A.: Local L 2-regularity of Riemann’s Fourier series. Ann. l’Inst. Fourier (2017, in press). Preprint, arXiv:1405.0810
28.
Triebel, H.: Theory of Function Spaces. Monographs in Mathematics, vol. 78, 284 pp. Birkhäuser, Basel (1983)
Metadata
Title
New Exponents for Pointwise Singularity Classification
Authors
Patrice Abry
Stéphane Jaffard
Roberto Leonarduzzi
Clothilde Melot
Herwig Wendt
Copyright Year
2017
Book
Recent Developments in Fractals and Related Fields

Print ISBN: 978-3-319-57803-3

Electronic ISBN: 978-3-319-57805-7

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-57805-7_1

Premium Partner

    Image Credits