English

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 LpL^p-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}
}

Comments

11 pages