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Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions
- Source :
- Anal. PDE 8, no. 3 (2015), 747-764
- Publication Year :
- 2014
- Publisher :
- arXiv, 2014.
-
Abstract
- We obtain some improved essentially sharp Kakeya-Nikodym estimates for eigenfunctions in two-dimensions. We obtain these by proving stronger related microlocal estimates involving a natural decomposition of phase space that is adapted to the geodesic flow.<br />Comment: 17 pages, 2 figures
- Subjects :
- Mathematics - Differential Geometry
Kakeya averages
Numerical Analysis
Pure mathematics
Applied Mathematics
010102 general mathematics
Mathematics::Classical Analysis and ODEs
eigenfunctions
58J51
35L20
Eigenfunction
Mathematics::Spectral Theory
01 natural sciences
Mathematics - Analysis of PDEs
Differential Geometry (math.DG)
Mathematics - Classical Analysis and ODEs
0103 physical sciences
Classical Analysis and ODEs (math.CA)
FOS: Mathematics
010307 mathematical physics
0101 mathematics
42B37
Analysis
Mathematics
Analysis of PDEs (math.AP)
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Anal. PDE 8, no. 3 (2015), 747-764
- Accession number :
- edsair.doi.dedup.....140eb21ff9f6894c94ca2fd80941cab2
- Full Text :
- https://doi.org/10.48550/arxiv.1409.1286