Eigenvalue estimates for a class of operators related to self-similar measures
Journées équations aux dérivées partielles (1994), article no. 11, 6 p. 
@article{JEDP_1994____A11_0,
     author = {Solomyak, Michael},
     title = {Eigenvalue estimates for a class of operators related to self-similar measures},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {11},
     pages = {1--6},
     publisher = {Ecole polytechnique},
     year = {1994},
     mrnumber = {95h:35163},
     zbl = {0881.58072},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1994____A11_0/}
}
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
SP  - 1
EP  - 6
PB  - Ecole polytechnique
UR  - http://www.numdam.org/item/JEDP_1994____A11_0/
LA  - en
ID  - JEDP_1994____A11_0
ER  - 
%0 Journal Article
%A Solomyak, Michael
%T Eigenvalue estimates for a class of operators related to self-similar measures
%J Journées équations aux dérivées partielles
%D 1994
%P 1-6
%I Ecole polytechnique
%U http://www.numdam.org/item/JEDP_1994____A11_0/
%G en
%F JEDP_1994____A11_0
Solomyak, Michael. Eigenvalue estimates for a class of operators related to self-similar measures. Journées équations aux dérivées partielles (1994), article  no. 11, 6 p. http://www.numdam.org/item/JEDP_1994____A11_0/

[F] W. Feller, An introduction to the probability theory and its applications, Vol. II, John Wiley & Sons, Inc., New York-London-Sydney-Toronto, 1971. | MR | Zbl

[H] J.E. Hutchinson, «Fractals and self-similarity», Indiana Univ. Math. J. 30 (1981) 713-747. | MR | Zbl

[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 | Zbl

[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 | Zbl

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

[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

[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

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

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

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

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