Uniform asymptotics of the eigenvalues and eigenfunctions of the Dirac system with an integrable potential

2016 ◽  
Vol 52 (8) ◽  
pp. 1000-1010 ◽  
Author(s):  
I. V. Sadovnichaya
Keyword(s):  
Uniform Asymptotics ◽  
Dirac System ◽  
Eigenvalues And Eigenfunctions ◽  
Integrable Potential ◽  
Asymptotics Of The Eigenvalues

scholarly journals Asymptotic Behavior of Solutions of the Dirac System with an Integrable Potential

2021 ◽  
Vol 93 (5) ◽  
Author(s):  
Łukasz Rzepnicki
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Parameter ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Dirac System ◽  
Eigenvalues And Eigenfunctions ◽  
Integrable Potential ◽  
Sturm Liouville ◽  
Complex Valued ◽  
Liouville Operators

AbstractWe consider the Dirac system on the interval [0, 1] with a spectral parameter $$\mu \in {\mathbb {C}}$$ μ ∈ C and a complex-valued potential with entries from $$L_p[0,1]$$ L p [ 0 , 1 ] , where $$1\le p$$ 1 ≤ p . We study the asymptotic behavior of its solutions in a strip $$|\mathrm{Im}\,\mu |\le d$$ | Im μ | ≤ d for $$\mu \rightarrow \infty $$ μ → ∞ . These results allow us to obtain sharp asymptotic formulas for eigenvalues and eigenfunctions of Sturm–Liouville operators associated with the aforementioned Dirac system.

Refined asymptotic formulas for eigenvalues and eigenfunctions of the Dirac system

2012 ◽  
Vol 85 (2) ◽  
pp. 240-242 ◽  
Author(s):  
M. Sh. Burlutskaya ◽  
V. P. Kurdyumov ◽  
A. P. Khromov
Keyword(s):  
Asymptotic Formulas ◽  
Dirac System ◽  
Eigenvalues And Eigenfunctions

scholarly journals Refined Asymptotic Formulas for Eigenvalues and Eigenfunctions of the Dirac System with Nondifferentiable Potential

2012 ◽  
Vol 12 (3) ◽  
pp. 22-30 ◽  
Author(s):  
Mariya Shaukatovna Burlutskaya ◽  
◽  
Vitalii Pavlovich Kurdyumov ◽  
Avgust Petrovich Khromov ◽  
◽  
...  
Keyword(s):  
Asymptotic Formulas ◽  
Dirac System ◽  
Eigenvalues And Eigenfunctions

Estimates of Riesz Constants for the Dirac System with an Integrable Potential

2018 ◽  
Vol 54 (6) ◽  
pp. 748-757 ◽  
Author(s):  
A. M. Savchuk ◽  
I. V. Sadovnichaya
Keyword(s):  
Dirac System ◽  
Integrable Potential
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