Eigenvalue estimates for a class of operators related to self-similar measures

Michael Solomyak

Journées équations aux dérivées partielles (1994)

  • Volume: 1994, page 1-6
  • ISSN: 0752-0360

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Solomyak, Michael. "Eigenvalue estimates for a class of operators related to self-similar measures." Journées équations aux dérivées partielles 1994 (1994): 1-6. <http://eudml.org/doc/93279>.

@article{Solomyak1994,
author = {Solomyak, Michael},
journal = {Journées équations aux dérivées partielles},
keywords = {eigenvalue distribution; self-similar measure; Sobolev space},
language = {eng},
pages = {1-6},
publisher = {Ecole polytechnique},
title = {Eigenvalue estimates for a class of operators related to self-similar measures},
url = {http://eudml.org/doc/93279},
volume = {1994},
year = {1994},
}

TY - JOUR
AU - Solomyak, Michael
TI - Eigenvalue estimates for a class of operators related to self-similar measures
JO - Journées équations aux dérivées partielles
PY - 1994
PB - Ecole polytechnique
VL - 1994
SP - 1
EP - 6
LA - eng
KW - eigenvalue distribution; self-similar measure; Sobolev space
UR - http://eudml.org/doc/93279
ER -

References

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  1. [F] W. Feller, An introduction to the probability theory and its applications, Vol. II, John Wiley & Sons, Inc., New York-London-Sydney-Toronto, 1971. Zbl0219.60003MR42 #5292
  2. [H] J.E. Hutchinson, «Fractals and self-similarity», Indiana Univ. Math. J. 30 (1981) 713-747. Zbl0598.28011MR82h:49026
  3. [K Lap] J. Kigami, M.L. Lapidus, «Weyl's problem for the spectral distribution of Laplacians on p.c.f. self-similar fractals», Commun. Math. Phys. 158 (1993) 93-125. Zbl0806.35130MR94m:58225
  4. [Lap] M. Lapidus, «Vibrations of fractal drums, the Riemann hypothesis, waves in fractal media and the Weyl-Berry conjecture», Ordinary and partial differential equations, Vol. 4, B.D. Sleeman and R.J. Jarvis (editors), Pitman Research Notes in Mathematics 289 (1993) 126-209. Zbl0830.35094MR95g:58247
  5. [Lau W] K.-S. Lau, J. Wang, «Mean quadratic variations and Fourier asymptotics of self-similar measures», Monat. Math. 115 (1993) 99-132. Zbl0778.28005MR94g:42018
  6. [Lev V] M. Levitin, D. Vassiliev, «Spectral asymptotics, renewal theorem and the Berry conjecture for a class of fractals» (1994) preprint. 
  7. [M] V. Maz'ja, Sobolev spaces, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1985. MR87g:46056
  8. [NS] K. Naimark, M. Solomyak, «On the eigenvalue behaviour for a class of operators related to self-similar measures on ℝd», submitted to C.R. Acad. Sci. Paris. Zbl0808.60038
  9. [R Sim] M. Reed, B. Simon, Methods of modern mathematical physics, Vol. IV, Academic Press, New York-San Francisco-London, 1978. Zbl0401.47001
  10. [SV] M. Solomyak, E. Verbitsky, «On a spectral problem related to self-similar measures», Bull. of London Math. Soc. (to appear). Zbl0823.34071
  11. [St1] R.S. Strichartz, «Self-similar measures and their Fourier transforms I», Indiana Univ. Math. J. 39 (1990) 797-817. Zbl0695.28003MR92k:42015
  12. [St2] R.S. Strichartz, «Self-similarity in harmonic analysis», preprint. 

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