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Eigenvalue estimates for a class of operators related to self-similar measures
Michael Solomyak
Journées équations aux dérivées partielles (1994), article no. 11, 6 p.
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MR: 95h:35163 | Zbl: 0881.58072
DOI: 10.5802/jedp.466
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@article{JEDP_1994____A11_0,
     author = {Michael Solomyak},
     title = {Eigenvalue estimates for a class of operators related to self-similar measures},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {11},
     publisher = {\'Ecole polytechnique},
     year = {1994},
     doi = {10.5802/jedp.466},
     zbl = {0881.58072},
     mrnumber = {95h:35163},
     language = {en},
     url = {https://jedp.centre-mersenne.org/articles/10.5802/jedp.466/}
}
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Michael Solomyak. Eigenvalue estimates for a class of operators related to self-similar measures. Journées équations aux dérivées partielles (1994), article  no. 11, 6 p. doi : 10.5802/jedp.466. https://jedp.centre-mersenne.org/articles/10.5802/jedp.466/
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[H] J.E. Hutchinson, «Fractals and self-similarity», Indiana Univ. Math. J. 30 (1981) 713-747. | MR: 82h:49026 | Zbl: 0598.28011

[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. | MR: 94m:58225 | Zbl: 0806.35130

[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. | MR: 95g:58247 | Zbl: 0830.35094

[Lau W] K.-S. Lau, J. Wang, «Mean quadratic variations and Fourier asymptotics of self-similar measures», Monat. Math. 115 (1993) 99-132. | MR: 94g:42018 | Zbl: 0778.28005

[Lev V] M. Levitin, D. Vassiliev, «Spectral asymptotics, renewal theorem and the Berry conjecture for a class of fractals» (1994) preprint.

[M] V. Maz'Ja, Sobolev spaces, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1985. | MR: 87g:46056

[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. | Zbl: 0808.60038

[R Sim] M. Reed, B. Simon, Methods of modern mathematical physics, Vol. IV, Academic Press, New York-San Francisco-London, 1978. | Zbl: 0401.47001

[SV] M. Solomyak, E. Verbitsky, «On a spectral problem related to self-similar measures», Bull. of London Math. Soc. (to appear). | Zbl: 0823.34071

[St1] R.S. Strichartz, «Self-similar measures and their Fourier transforms I», Indiana Univ. Math. J. 39 (1990) 797-817. | MR: 92k:42015 | Zbl: 0695.28003

[St2] R.S. Strichartz, «Self-similarity in harmonic analysis», preprint.

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