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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
Zbl 0486.35026
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