A sharp weightedL2-estimate for the solution to the time-dependent Schrödinger equation
- Cite this article as:
- Walther, B.G. Ark. Mat. (1999) 37: 381. doi:10.1007/BF02412222
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Our theorems can be generalized to the case where the exp(it|ξ|2) is replaced by exp(it|ξ|a),a≠2.
The proof uses Parseval's formula onR, orthogonality arguments arising from decomposingL2(Rn) using spherical harmonics and a uniform estimate for Bessel functions. Homogeneity arguments are used to show that results are sharp with respect to regularity.