Spectral asymptotics for Krein–Feller operators with respect to 𝑉-variable Cantor measures
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AbstractWe study the limiting behavior of the Dirichlet and Neumann eigenvalue counting function of generalized second-order differential operators {\frac{\mathop{}\!d}{\mathop{}\!d\mu}\frac{\mathop{}\!d}{\mathop{}\!dx}}, where μ is a finite atomless Borel measure on some compact interval {[a,b]}. Therefore, we firstly recall the results of the spectral asymptotics for these operators received so far. Afterwards, we make a proposition about the convergence behavior for so-called random V-variable Cantor measures.
1985 ◽
Vol 25
(4)
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pp. 659-681
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1999 ◽
Vol 59
(1)
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pp. 227-251
1983 ◽
Vol 8
(6)
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pp. 643-665
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2016 ◽
Vol 52
(12)
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pp. 1563-1574
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