Integral equations between theory and practice: the cases of Italy and France to 1920
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 Archival material, letters and unpublished manuscripts (in particular parts of Boggio's contribution to the Prix Vaillant, which comes as an appendix), is broadly included.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.
partial differential equations in elasticity theory
scientific article; zbMATH DE number 6353778
scientific article