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Differentiability of generalized Fourier transforms associated with Schrödinger operators. (English) Zbl 0612.35004
In a previous paper [J. Reine Angew. Math. 337, 18-67 (1982; Zbl 0486.35026)] the author developed a theory of generalized Fourier transform \({\mathcal F}\) associated with the Schrödinger operator \(H=- \Delta +V(x)\) in \(L^ 2({\mathbb{R}}^ n)\) (n\(\geq 2)\) with a long-range potential V(x). The main purpose of this paper is to prove that for \(f\in L^{2,N+r}\) \((r>\), \(N\in {\mathbb{N}})\), (\({\mathcal F}f)(\xi)\) is N-times differentiable with respect to \(\xi\neq 0\).
Reviewer: G.Moroşanu

MSC:
35A22 Transform methods (e.g., integral transforms) applied to PDEs
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
35J10 Schrödinger operator, Schrödinger equation
Citations:
Zbl 0486.35026
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