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 Zap. Nauchn. Sem. POMI, 2018, Volume 477, Pages 129–135 (Mi znsl6741)

On spectral asymptotics of the Sturm–Liouville problem with self-conformal singular weight with strong bounded distortion property

U. R. Freiberga, N. V. Rastegaevb

a Institut für Stochastik und Anwendungen, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
b Chebyshev Laboratory, St. Petersburg State University, 14th Line 29b, 199178 St. Petersburg, Russia

Abstract: Spectral asymptotics of the Neumann problem for the Sturm–Liouville equation with a singular self-conformal weight measure is considered under the assumption of a stronger version of the bounded distortion property for the conformal iterated function system corresponding to the weight measure. The power exponent of the main term of the eigenvalue counting function asymptotics is obtained. This generalizes the result obtained by T. Fujita (Taniguchi Symp. PMMP Katata, 1985) in the case of self-similar (self-affine) measure.

Key words and phrases: spectral asymptotics, self-conformal measures.

 Funding Agency Grant Number Russian Science Foundation 14-21-00035 Research is supported by the Russian Science Foundation grant No. 14-21-00035.

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Citation: U. R. Freiberg, N. V. Rastegaev, “On spectral asymptotics of the Sturm–Liouville problem with self-conformal singular weight with strong bounded distortion property”, Boundary-value problems of mathematical physics and related problems of function theory. Part 47, Zap. Nauchn. Sem. POMI, 477, POMI, St. Petersburg, 2018, 129–135

Citation in format AMSBIB
\Bibitem{FreRas18} \by U.~R.~Freiberg, N.~V.~Rastegaev \paper On spectral asymptotics of the Sturm--Liouville problem with self-conformal singular weight with strong bounded distortion property \inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~47 \serial Zap. Nauchn. Sem. POMI \yr 2018 \vol 477 \pages 129--135 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6741}