Asymptotics of the eigenvalues for exponentially parameterized pentadiagonal matrices

2020 ◽  
Vol 27 (6) ◽  
Author(s):  
Hanieh Tavakolipour ◽  
Fatemeh Shakeri
Keyword(s):  
Asymptotics Of The Eigenvalues

Jacobi Matrices and the Spectrum of the Neumann Operator on a Family of Riemann Surfaces

1993 ◽  
Vol 45 (4) ◽  
pp. 709-726
Author(s):  
Julian Edward
Keyword(s):  
Harmonic Function ◽  
Riemann Surfaces ◽  
Smooth Manifold ◽  
Hypergeometric Functions ◽  
Normal Derivative ◽  
Jacobi Matrices ◽  
Uniform Bounds ◽  
Neumann Operator ◽  
Direct Sum ◽  
Asymptotics Of The Eigenvalues

AbstractThe Neumann operator is an operator on the boundary of a smooth manifold which maps the boundary value of a harmonic function to its normal derivative. The spectrum of the Neumann operator is studied on the curves bounding a family of Riemann surfaces. The Neumann operator is shown to be isospectral to a direct sum of symmetric Jacobi matrices, each acting on l2(ℤ). The Jacobi matrices are shown to be isospectral to generators of bilateral, linear birth-death processes. Using the connection between Jacobi matrices and continued fractions, it is shown that the eigenvalues of the Neumann operator must solve a certain equation involving hypergeometric functions. Study of the equation yields uniform bounds on the eigenvalues and also the asymptotics of the eigenvalues as the curves degenerate into a wedge of circles.

Asymptotics of the eigenvalues of Sturm-Liouville problem

2016 ◽  
Vol 51 (4) ◽  
pp. 173-181
Author(s):  
T. N. Harutyunyan
Keyword(s):  
Liouville Problem ◽  
Sturm Liouville ◽  
Asymptotics Of The Eigenvalues

scholarly journals Asymptotics of the eigenvalues of two-diagonal Jacobi matrices

2005 ◽  
Vol 77 (1-2) ◽  
pp. 283-287 ◽  
Author(s):  
R. V. Kozhan
Keyword(s):  
Jacobi Matrices ◽  
Asymptotics Of The Eigenvalues

ASYMPTOTICS OF THE EIGENVALUES AND REGULARIZED TRACE OF THE FIRST-ORDER STURM–LIOUVILLE OPERATOR WITH δ-POTENTIAL

2016 ◽  
pp. 104-113
Author(s):  
Natal’ya Konechnaya ◽  
◽  
Tat’yana Safonova ◽  
Rena Tagirova
Keyword(s):  
Liouville Operator ◽  
Regularized Trace ◽  
First Order ◽  
Sturm Liouville ◽  
Asymptotics Of The Eigenvalues

scholarly journals Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions

2021 ◽  
Vol 49 (4) ◽  
Author(s):  
Khalil Chouk ◽  
Willem van Zuijlen
Keyword(s):  
White Noise ◽  
Two Dimensions ◽  
Anderson Hamiltonian ◽  
Asymptotics Of The Eigenvalues

scholarly journals Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Manfred Möller ◽  
Bertin Zinsou
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Imaginary Axis ◽  
Order Ordinary Differential Equation ◽  
Eigenvalue Parameter ◽  
Upper Half Plane ◽  
Parameter Dependent ◽  
Asymptotics Of The Eigenvalues

Considered is a regular fourth order ordinary differential equation which depends quadratically on the eigenvalue parameterλand which has separable boundary conditions depending linearly onλ. It is shown that the eigenvalues lie in the closed upper half plane or on the imaginary axis and are symmetric with respect to the imaginary axis. The first four terms in the asymptotic expansion of the eigenvalues are provided.

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