Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T05:05:19.523Z Has data issue: false hasContentIssue false

11 - On the Existence and Uniqueness of Self-Adjoint Realizations of Discrete (Magnetic) Schrödinger Operators

Published online by Cambridge University Press:  14 August 2020

By
Marcel Schmidt
Edited by
Matthias Keller ,
Daniel Lenz  and
Radoslaw K. Wojciechowski
Matthias Keller
Affiliation:
Universität Potsdam, Germany
Daniel Lenz
Affiliation:
Universität Potsdam, Germany
Radoslaw K. Wojciechowski
Affiliation:
York College of the City University of New York
Get access

Summary

In this expository paper weanswertwo fundamental questions concerning discrete magnetic Schrödinger operator associated with weighted graphs. We discuss when formal expressions of such operators give rise to self-adjoint operators, i.e., when they have self-adjoint realizations. If such self-adjoint realizations exist, we explore when they are unique.

Keywords

discrete Laplaciandiscrete magnetic Schrödinger operatoressential self-adjointnessuniqueness of self-adjoint realizationsMarkov uniquenessmaximal Markovian extension
Type
Chapter
Information
Analysis and Geometry on Graphs and Manifolds , pp. 250 - 327
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×