Celebratio Mathematica — Calderón

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Works connected to Allen Devinatz

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A. P. Calderón and A. Devinatz: “On Fourier–Stieltjes transforms,” Can. J. Math. 7 (1955), pp. 453–461. MR 0073747 Zbl 0065.34102 article

Let \( \mathcal{M} \) be the class of bounded non-decreasing functions defined on the real line which are normalized by the conditions \[ \phi(-\infty) = 0, \quad \phi(t+0) = \phi(t) .\] Let \( \mathcal{F} \) be the class of Fourier–Stieltjes transforms of elements of \( \mathcal{M} \), i.e. the elements of \( \mathcal{M} \) and \( \mathcal{F} \) are connected by the relation \[ \Phi(x) = \int e^{itx}d\phi(t), \] where \( \phi \in \mathcal{M} \) and \( \Phi \in \mathcal{F} \). It is well known, and easy to verify that this mapping from \( \mathcal{M} \) to \( \mathcal{F} \) is one to one [Bochner 1932, p.67, Satz 18].

It is the purpose of this paper to give various topologies to \( \mathcal{F} \) and \( \mathcal{M} \) so that the mapping from \( \mathcal{F} \) to \( \mathcal{M} \) will be continuous or at least continuous at certain points of \( \mathcal{F} \) depending on the topologies. The topologies which we shall have occasion to use are enumerated below.

A. Calderón and A. Devinatz: “Sur certaines courbes dans l’espace de Hilbert” [On certain curves on Hilbert space], C. R. Acad. Sci. Paris 241 (1955), pp. 539–541. MR 0071741 Zbl 0064.36803 article

A. P. Calderón and A. Devinatz: “Sur certaines courbes à coubure constante dans l’espace de Hilbert” [On certain curves of constant curvature on Hilbert space], C. R. Acad. Sci. Paris 241 (1955), pp. 586–587. MR 0071742 Zbl 0064.36804 article