Volterra’s functionals and covariant cohesion of space
نویسنده
چکیده
Volterra’s principle of passage from finiteness to infinity is far less limited than a linearized construal of it might suggest; I outline in Section III a nonlinear version of the principle with the help of category theory. As necessary background I review in Section II some of the mathematical developments of the period 1887-1913 in order to clarify some more recent advances and controversies which I discuss in Section I. I The immediate impetus to this historical exploration came from two articles by Gaetano Fichera. The resulting line of study needs to be deepened and considered in more detail, but it already supports certain conclusions concerning the precise methodological direction of global analysis. These methodological conclusions can perhaps be tested on the ample material provided by the important new book by Kriegl and Michor, just published by the AMS [17]. On that basis we can hopefully begin a serious reply to the challenge of ‘I difficili rapporti fra l’analisi funzionale e la fisica matematica’. Some of those difficulties are outlined in the article [8] (with that title) by Fichera. The other article by Fichera, ‘Vito Volterra and the birth of functional analysis’ [9], is basically a re-affirmation of the role of the Volterra school in the development of modern analysis, in response to Dieudonné’s [6] : We must finally mention the first attempt at ‘Functional Analysis’ of the young Volterra in 1887, to which, under the influence of Hadamard, has been attributed an exaggerated historical importance. More specifically, in connection with Volterra’s notion of the derivative of a functional, Dieudonné further states:
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تاریخ انتشار 1998