@incollection{JEDP_1994____A11_0, author = {Solomyak, Michael}, title = {Eigenvalue estimates for a class of operators related to self-similar measures}, booktitle = {}, series = {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://archive.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://archive.numdam.org/item/JEDP_1994____A11_0/ LA - en ID - JEDP_1994____A11_0 ER -
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://archive.numdam.org/item/JEDP_1994____A11_0/
[F] An introduction to the probability theory and its applications, Vol. II, John Wiley & Sons, Inc., New York-London-Sydney-Toronto, 1971. | MR | Zbl
,[H] «Fractals and self-similarity», Indiana Univ. Math. J. 30 (1981) 713-747. | MR | Zbl
,[K Lap] «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] «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] «Mean quadratic variations and Fourier asymptotics of self-similar measures», Monat. Math. 115 (1993) 99-132. | MR | Zbl
, ,[Lev V] «Spectral asymptotics, renewal theorem and the Berry conjecture for a class of fractals» (1994) preprint.
, ,[M] Sobolev spaces, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1985. | MR
,[NS] «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] Methods of modern mathematical physics, Vol. IV, Academic Press, New York-San Francisco-London, 1978. | Zbl
, ,[SV] «On a spectral problem related to self-similar measures», Bull. of London Math. Soc. (to appear). | Zbl
, ,[St1] «Self-similar measures and their Fourier transforms I», Indiana Univ. Math. J. 39 (1990) 797-817. | MR | Zbl
,[St2] «Self-similarity in harmonic analysis», preprint.
,