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8 results on '"mathieu operator"'

1. Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients

Author

Encinas A.M. and Jiménez M.J.

Subjects
discrete schrödinger operator, mathieu operator, periodic coefficients, bounded solutions, 39a12, 39a70, Mathematics, QA1-939
Abstract

In this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.

Published
2018
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3. Cantor Spectrum for Quasi-Periodic Schrödinger Operators

Author

Puig, Joaquim, Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, B.-G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, Asch, Joachim, editor, and Joye, Alain, editor

Published
2006
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4. Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients

Author

María José Jiménez Jiménez, Andrés Marcos Encinas Bachiller, Universitat Politècnica de Catalunya. Departament de Matemàtiques, and Universitat Politècnica de Catalunya. COMPTHE - Combinatòria i Teoria Discreta del Potencial pel control de paràmetres en xarxes

Subjects
bounded solutions, General Mathematics, 010102 general mathematics, Matemàtiques i estadística [Àrees temàtiques de la UPC], 010103 numerical & computational mathematics, Mathematics::Spectral Theory, 39a12, 01 natural sciences, discrete schrödinger operator, mathieu operator, 39a70, Bounded function, Equacions diferencials lineals, periodic coefficients, QA1-939, Applied mathematics, Order (group theory), Differential equations, Linear, 0101 mathematics, Self-adjoint operator, Mathematics
Abstract

In this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.

Published
2018

5. Refined asymptotics of the spectral gap for the Mathieu operator

Author

Anahtarci, Berkay and Djakov, Plamen

Subjects
*ASYMPTOTIC expansions, *SPECTRAL theory, *OPERATOR theory, *MATHEMATICAL formulas, *EIGENVALUES, *PERIODIC functions, *BOUNDARY value problems
Abstract

Abstract: The Mathieu operator considered with periodic or anti-periodic boundary conditions has, close to for large enough , two periodic (if is even) or anti-periodic (if is odd) eigenvalues , . For fixed , we show that This result extends the asymptotic formula of Harrell–Avron–Simon by providing more asymptotic terms. [Copyright &y& Elsevier]

Published
2012
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6. Adiabatic limits on Riemannian Sol-manifolds.

Author

Yakovlev, A. A.

Subjects
*MATHEMATICAL analysis, *MANIFOLDS (Mathematics), *RIEMANNIAN manifolds, *DISTRIBUTION (Probability theory), *MATRICES (Mathematics)
Abstract

The article presents a study that investigates the adiabatic limits on Riemannian Sol-manifolds. It refers to the examination of diverse properties of the family of Riemannian manifolds as the passage to adiabatic limit. Result shows the evaluation of the asymptotic behavior of the spectrum distribution function.

Published
2008
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8. Refined asymptotics of the spectral gap for the Mathieu operator

Author

Berkay Anahtarci and Plamen Borissov Djakov

Subjects
Operator (physics), Spectral gap asymptotics, Applied Mathematics, Asymptotic formula, Spectral gap, Boundary value problem, Eigenvalues and eigenvectors, Analysis, Mathematics, Mathematical physics, Mathieu operator
Abstract

The Mathieu operator L ( y ) = − y ″ + 2 a cos ( 2 x ) y , a ∈ C , a ≠ 0 , considered with periodic or anti-periodic boundary conditions has, close to n 2 for large enough n , two periodic (if n is even) or anti-periodic (if n is odd) eigenvalues λ n − , λ n + . For fixed a , we show that λ n + − λ n − = ± 8 ( a / 4 ) n [ ( n − 1 ) ! ] 2 [ 1 − a 2 4 n 3 + O ( 1 n 4 ) ] , n → ∞ . This result extends the asymptotic formula of Harrell–Avron–Simon by providing more asymptotic terms.

Published
2012
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