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SOURCES Manuscript Volumes and Lecture Notes of Salvatore Pincherle View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector HISTORIA MATHEMATICA 16 (1989) 379-380 SOURCES This department welcomes correspondence, brief announcements, and article-length de- scriptions of collections of publications, correspondence, and archival material relevant to the history of mathematics. Manuscripts describing major collections (covering such matters as acquisition, size, scope, state of cataloging, and current and future availability) should follow the same standards as other articles. They will be abstracted and indexed like other articles, and authors will be supplied with free reprints. Manuscript Volumes and Lecture Notes of Salvatore Pincherle By Umberto Bottazzini and Stefano Francesconi Dipartimento di Matematica, Universitd degli studi di Bologna, Piazza di Porta S. Donato, 5, 40127 Bologna, Italy AMS 1985 subject classifications: OlA55, OlA60, 46-03. Salvatore Pincherle (Trieste, 1853-Bologna, 1936) was one of the leading Italian mathematicians of his generation. He is remembered for his contributions (e.g., in 1886, 1887, 1896, 1900, and 1901) to the early development of functional analysis. He also founded the UMI (the Italian Mathematical Society) and organized the International Congress of Mathematicians held in Bologna in 1928. Pincherle completed his undergraduate studies in Marseille, France, where Pincherle’s family had gone to live some years after his birth. Between 1869 and 1874 Pincherle was a student at the Scuola Normale Superiore in Pisa. Here he attended classes taught by E. Betti and U. Dini. Three years later, Pincherle went to Berlin, where he studied with K. Weierstrass. After returning to Italy, Pincherle published his well-known Saggio di una introduzione alla teoria delle funzioni anatitiche second0 i principi de1 Prof. K. Weierstrass [Pincherle 18801. In 1882, Pincherle became professor of “Matematiche complementari” at Bo- logna University. His lectures were the first in Italy to explain the theory of analytic functions from a Weierstrassian viewpoint. In addition to his publications, Pincherle’s scientific activities are documented in 55 manuscript volumes preserved in the Bortolotti library (Department of Math- ematics, Bologna University). Here there are also various lecture notes (by Borto- lotti and others) from Pincherle’s courses. Generally each volume covers about one year of Pincherle’s scientific activities. Each volume is also generally divided into two sections. In the first there are the Appunti e saggi uari d’AnaZisi; these are the drafts of Pincherle’s works. The second is entitled Estratti ed appunti di Zetture and comprises a collection of remarks that Pincherle has quoted from the 379 03 150860/89 $3.00 Copyright 0 1989 by Academic Press, Inc. All rights of reproduction in any form reserved. 380 SOURCES HM 16 works of contemporary mathematicians. Finally, some volumes contain notes from Pincherle’s courses. The contents of the 55 volumes are summarized in the following list. Volumes I-II (from January 1882 to October 1891). These volumes contain the first studies on definite integrals [Pincherle 1883- 1884a,b J, Laplace transforms [Pincherle 18871, recursion sequences [Pincherle 1889a], and continuous fractions [Pincherle 1889b]. Volume 12. This volume is a collection of the notes from lectures on elliptic functions, analytic functions, and hypergeometric functions given by Pincherle between 1891 and 1894. Volumes 13-22 (from November 1991 to November 1900). In these volumes are various drafts of Le operazioni distributive e le loro applicazioni all’analisi [Pincherle 190 11. Volume 23. This volume contains the notes from lectures on analytic functions given by Pincherle between 1904 and 1909. Volumes 24-33 (from December 1900 to January 1911). These volumes include various drafts of the Funktionaloperationen und Gleichungen [Pincherle 19061 and the courses on the theory of analytic functions given by Pincherle between 1904 and 1909. Volumes 34-43 (from February 1911 to September 1922). In these volumes there are various drafts of Gli elementi della teoria delle funzioni analitiche [Pin- cherle 19221. Volumes 44-55 (from October 1922 to July 1936). In these volumes there are notes on the theory of analytic functions, calculus of finite differences, and functional calculus. There are also various lecture notes from Pincherle’s courses and lectures. According to the wishes of Pincherle himself, his correspondence was de- stroyed after his death. Only a few letters have survived and we will publish them in a future paper. REFERENCES Pincherle, S. 1880. Saggio di una introduzione alla teoria delle funzioni analitiche second0 i principi de1 Prof. C. Weierstrass. Giornale di Matematiche 18, 178-254, 317-357. 1883-1884a. Sui sistemi di funzioni analitiche e le serie formate coi medesimi. Memoria I. Annali di Matematica pura ed applicata (Milano) 12(2), 11-41. 1883-1884b. Sui sistemi di funzioni analitiche e gli sviluppi in serie formati coi medesimi. Memoria II. Annali di Matematica pura ed applicata (Milano) l2(2), 107-133. 1887. Della trasformazione di Lapiace e di alcune sue applicazioni. Memorie della R. Accade- mia delle Scienze dell’lstituto di Bologna 8(4), 125-143. 1889a. I sistemi ricorrenti di prim’ordine e di second0 grado. Atti della R. Accademia dei Lincei, Rendiconti della Classe di Scienze Fisiche, Matematiche e Naturali (Roma) S(4), 8-12. 1889b. Alcuni teoremi sulle frazioni continue. Atti della R. Accademia dei Lincei, Rendiconti della Classa di Scienze Fisiche, Matematiche e Naturali (Roma) 5(4), 640-643. 1901. Le operazioni distributive e le loro applicazioni all’analisi. Bologna: Zanichelli. 1906. Funktionaloperationen und Gleichungen. Encyklopiidie der mathematischen Wissen- schaften mit Einschluss ihrer Anwendungen 2, 761-817. 1922. Gli elementi della teoria delle funzioni analitiche, Parte I. Bologna: Zanichelli. .
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