Electron. J. Differential Equations, Vol. 2018 (2018), No. 162, pp. 1-12.

Exponential estimates for quantum graphs

Setenay Akduman, Alexander Pankov

The article studies the exponential localization of eigenfunctions associated with isolated eigenvalues of Schrodinger operators on infinite metric graphs. We strengthen the result obtained in [3] providing a bound for the rate of exponential localization in terms of the distance between the eigenvalue and the essential spectrum. In particular, if the spectrum is purely discrete, then the eigenfunctions decay super-exponentially.

Submitted July 14, 2018. Published September 10, 2018.
Math Subject Classifications: 34B45, 34L40, 81Q35.
Key Words: Infinite metric graph; Schrodinger operator; eigenfunction; exponential decay.

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Setenay Akduman
Department of Mathematics
Izmir Democracy University
Izmir, 35140, Turkey
email: setenay.akduman@idu.edu.tr
Alexander Pankov
Department of Mathematics
Morgan State University
Baltimore, MD 21251, USA
email: alexander.pankov@morgan.edu

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