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Strichartz estimates for the wave and Schrödinger equations with potentials of critical decay. (English) Zbl 1084.35014
Summary: We prove weighted $$L^2$$ estimates for the solutions of linear Schrödinger and wave equations with potentials that decay like $$|x|^{-2}$$ for large $$x$$, by deducing them from estimates on the resolvent of the associated elliptic operator. We then deduce Strichartz estimates for these equations.

##### MSC:
 35B45 A priori estimates in context of PDEs 35L15 Initial value problems for second-order hyperbolic equations 35Q40 PDEs in connection with quantum mechanics 35L05 Wave equation 35G10 Initial value problems for linear higher-order PDEs
##### Keywords:
resolvent estimates
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