Spectral Multipliers for Schrödinger Operators

Authors

Shijun Zheng, Georgia Southern UniversityFollow

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