Mathematical Sciences: Faculty Publications
Spectral Multipliers for Schrödinger Operators
Document Type
Article
Publication Date
2010
Publication Title
Illinois Journal of Mathematics
ISSN
0019-2082
Abstract
We prove a sharp Hörmander multiplier theorem for Schrödinger operators H = −Δ + V on ℝn. The result is obtained under certain condition on a weighted L∞ estimate, coupled with a weighted L2 estimate for H, which is a weaker condition than that for nonnegative operators via the heat kernel approach. Our approach is elaborated in one dimension with potential V belonging to certain critical weighted L1 class. Namely, we assume that ∫(1 + |x|)|V(x)| dx is finite and H has no resonance at zero. In the resonance case, we assume ∫(1 + |x|2)|V(x)| dx is finite.
Recommended Citation
Zheng, Shijun.
2010.
"Spectral Multipliers for Schrödinger Operators."
Illinois Journal of Mathematics, 54 (2): 621-647.
source: http://projecteuclid.org/euclid.ijm/1318598675
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/259
Copyright
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