Wawrzyńczyk, Antoni On the infinitesimal generator of the Fourier transform. (English) Zbl 0759.42007 An. Inst. Mat., Univ. Nac. Autón. Méx. 30, 83-88 (1990). In the group \(U(L^ 2(\mathbb{R}))\) for all unitary operators in \(L^ 2(\mathbb{R})\) the Fourier transform can be joined with the identity by means of a 1-parameter subgroup. The author uses the irreducibility of the Schrödinger representation to prove that \(H:=i{\pi\over 4}\left[{d^ 2\over dx^ 2}-x^ 2+id\right]\) is the infinitesimal generator of this subgroup. Reviewer: B.P.Duggal (Lesotho) MSC: 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 47D03 Groups and semigroups of linear operators Keywords:Fourier transform; 1-parameter subgroup; Schrödinger representation; infinitesimal generator PDFBibTeX XMLCite \textit{A. Wawrzyńczyk}, An. Inst. Mat., Univ. Nac. Autón. Méx. 30, 83--88 (1990; Zbl 0759.42007)