Vol. 9, No. 4, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 7, 1539–1791
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
Cover
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Resonance free regions for nontrapping manifolds with cusps

Kiril Datchev

Vol. 9 (2016), No. 4, 907–953
Abstract

We prove resolvent estimates for nontrapping manifolds with cusps which imply the existence of arbitrarily wide resonance free strips, local smoothing for the Schrödinger equation, and resonant wave expansions. We obtain lossless limiting absorption and local smoothing estimates, but the estimates on the holomorphically continued resolvent exhibit losses. We prove that these estimates are optimal in certain respects.

Keywords
cusp, resonances, resolvent, scattering, waves
Mathematical Subject Classification 2010
Primary: 58J50
Milestones
Received: 16 December 2015
Accepted: 26 February 2016
Published: 3 July 2016
Authors
Kiril Datchev
Mathematics Department
Purdue University
150 N. University Street
West Lafayette, IN 47907
United States