Integral equations between theory and practice: the cases of Italy and France to 1920
type: Item
instance of: scholarly article
title: Integral equations between theory and practice: the cases of Italy and France to 1920
zbMATH Open document ID: 1346.01014
published in: Archive for History of Exact Sciences
publication date: 2014-10-10T00:00:00Z
review text: The paper gives a broad view of the theory of integral equations and its reception as an important and fashionable new discipline in the years before World War I, under the strong influence of the pioneering contributions by the Swede Ivar Fredholm since 1899. The authors stress the roots of the theory in the older theory of partial differential equations, as developed for instance by Fredholm himself but also by Volterra and Levi-Civita. These have hitherto found less attention by historians than the conceptual implications of Fredholm's work as one of the precursors to functional analysis, particularly through the Hilbert school. The authors also point repeatedly to the method of successive approximation (Picard and others) which stimulated the interest in integral equations, partly as a reformulation of older problems particularly in elasticity theory. The work of lesser known Italian analysts such as Tommaso Boggio and Giuseppe Lauricella is looked at in some detail. They shared the French Prix Vaillant in 1907 together with Jacques Hadamard and Arthur Korn for their work on the vibration of elastic plates. Archival material, letters and unpublished manuscripts (in particular parts of Boggio's contribution to the Prix Vaillant, which comes as an appendix), is broadly included. The authors investigate also parts of the process of the reception of integral equations, for instance in the work of Maxime Bôcher in the U.S.
reviewed by: Reinhard Siegmund-Schultze
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 45-03
zbMATH DE Number: 6353778
zbMATH Keywords: integral equations before WWI
zbMATH Keywords: Fredholm theory
zbMATH Keywords: partial differential equations in elasticity theory
zbMATH Keywords: successive approximations
zbMATH Keywords: Prix Vaillant
MaRDI profile type: Publication
full work available at URL: s00407-013-0132-2
OpenAlex ID: W2034854922
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DOI: 10.1007/S00407-013-0132-2
author: T. Archibald
author: R. Tazzioli
description: scientific article; zbMATH DE number 6353778