Spectral asymptotics of polynomial pencils of differential operators in bounded domains

1991 ◽  
Vol 25 (1) ◽  
pp. 5-16 ◽  
Author(s):  
K. Kh. Boimatov ◽  
A. G. Kostyuchenko
Keyword(s):  
Differential Operators ◽  
Spectral Asymptotics ◽  
Bounded Domains

Spectral asymptotics for Krein–Feller operators with respect to 𝑉-variable Cantor measures

2020 ◽  
Vol 32 (1) ◽  
pp. 121-138
Author(s):  
Lenon Alexander Minorics
Keyword(s):  
Borel Measure ◽  
Differential Operators ◽  
Counting Function ◽  
Second Order ◽  
Spectral Asymptotics ◽  
Compact Interval ◽  
Limiting Behavior ◽  
Convergence Behavior ◽  
Neumann Eigenvalue

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.

Spectral asymptotics and trace formulas for differential operators with unbounded coefficients

2008 ◽  
Vol 44 (12) ◽  
pp. 1691-1700
Author(s):  
Kh. Kh. Murtazin ◽  
V. A. Sadovnichii ◽  
R. Z. Tul’kubaev
Keyword(s):  
Differential Operators ◽  
Spectral Asymptotics ◽  
Trace Formulas ◽  
Unbounded Coefficients
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