Remote access

How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

   1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

   1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

   2. Complete and sign the license agreement.

   3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2294  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046
Email: cust-serv@ams.org

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

Powered by MathJax

On some aspects of oscillation theory and geometry


About this Title

Bruno Bianchini, Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Via Trieste 63, I-35121 Padova, Italy, Luciano Mari, Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, I-20133 Milano, Italy and Marco Rigoli, Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, I-20133 Milano, Italy

Publication: Memoirs of the American Mathematical Society
Publication Year: 2013; Volume 225, Number 1056
ISBNs: 978-0-8218-8799-8 (print); 978-1-4704-1056-8 (online)
DOI: http://dx.doi.org/10.1090/S0065-9266-2012-00681-2
Published electronically: December 13, 2012
Keywords:Oscillation, spectral theory, index, Schrodinger operator, uncertainty principle, compactness, immersions, comparison
MSC: Primary 34K11, 58C40, 35J15; Secondary 35J10, 53C21, 57R42

View full volume PDF

View other years and numbers:

Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. The Geometric setting
  • Chapter 3. Some geometric examples related to oscillation theory
  • Chapter 4. On the solutions of the ODE $(vz’)’ + Avz = 0$
  • Chapter 5. Below the critical curve
  • Chapter 6. Exceeding the critical curve
  • Chapter 7. Much above the critical curve

Abstract


The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation we prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep our investigation basically self-contained we also collect some, more or less known, material which often appears in the literature in various forms and for which we give, in some instances, new proofs according to our specific point of view.

References [Enhancements On Off] (What's this?)


Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia