Title

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.

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