Geodesic
On Spectral Asymptotics of the Neumann Problem for the Sturm–Liouville Equation with Arithmetically Self-Similar Weight of a Generalized Cantor Type
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 1, pp. 85-88 Cet article a éte moissonné depuis la source Math-Net.Ru

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Spectral asymptotics of the Sturm–Liouville problem with an arithmetically self-similar singular weight is considered. Previous results by A. A. Vladimirov and I. A. Sheipak, and also by the author, rely on the spectral periodicity property, which imposes significant restrictions on the self-similarity parameters of the weight. This work introduces a new method for estimating the eigenvalue counting function. This makes it possible to consider a much wider class of self-similar measures.
Keywords: spectral asymptotics, semi-similar measure. 
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N. V. Rastegaev. On Spectral Asymptotics of the Neumann Problem for the Sturm–Liouville Equation with Arithmetically Self-Similar Weight of a Generalized Cantor Type. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 1, pp. 85-88. http://geodesic.mathdoc.fr/item/FAA_2018_52_1_a10/

[1] A. A. Vladimirov, I. A. Sheipak, Funkts. analiz i ego pril., 47:4 (2013), 18–29 | DOI | MR | Zbl

[2] N. V. Rastegaev, Zap. nauchn. sem. POMI, 425 (2014), 86–98

[3] M. G. Krein, DAN SSSR, 76:3 (1951), 345–348 | Zbl

[4] M. Solomyak, E. Verbitsky, Bull. London Math. Soc., 27:3 (1995), 242–248 | DOI | MR | Zbl

[5] J. Kigami, M. L. Lapidus, Comm. Math. Phys., 158:1 (1991), 93–125 | DOI | MR

[6] A. I. Nazarov, Zap. nauch. sem. POMI, 311 (2004), 190–213 | Zbl

[7] A. A. Vladimirov, Algebra i analiz, 27:2 (2015), 83–95

[8] I. A. Sheipak, Matem. zametki, 81:6 (2007), 924–938 | DOI | MR | Zbl

[9] J. E. Hutchinson, Indiana Univ. Math. J., 30:5 (1981), 713–747 | DOI | MR | Zbl

[10] A. A. Vladimirov, Zh. vychisl. matem. i matem. fiz., 49:9 (2009), 1609–1621 | MR | Zbl