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We study the two dimensional Schrödinger operator, , in the weighted setting when there is a resonance of the first kind at zero energy. In particular, we show that if and there is only s-wave resonance at zero of , then
with . Here , where is an s-wave resonance function. We also extend this result to wave and matrix Schrödinger equations with potentials under similar conditions.
Cite this article
Ebru Toprak, A weighted estimate for two dimensional Schrödinger, matrix Schrödinger, and wave equations with resonance of the first kind at zero energy. J. Spectr. Theory 7 (2017), no. 4, pp. 1235–1284DOI 10.4171/JST/189