A note on $L^p$-norms of quasi-modes
Analysis of PDEs
2016-12-13 v1 Classical Analysis and ODEs
Abstract
In this note we show how improved -estimates for certain types of quasi-modes are naturally equaivalent to improved operator norms of spectral projection operators associated to shrinking spectral intervals of the appropriate scale. Using this, one can see that recent estimates that were stated for eigenfunctions also hold for the appropriate types of quasi-modes.
Keywords
Cite
@article{arxiv.1401.0345,
title = {A note on $L^p$-norms of quasi-modes},
author = {Christopher D. Sogge and Steve Zelditch},
journal= {arXiv preprint arXiv:1401.0345},
year = {2016}
}
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11 pages