Federico Cafiero (24 May 1914 – 7 May 1980) was an Italian mathematician known for his contributions in real analysis, measure and integration theory, and in the theory of ordinary differential equations. In particular, generalizing the Vitali convergence theorem, the Fichera convergence theorem and previous results of Vladimir Mikhailovich Dubrovskii, he proved a necessary and sufficient condition for the passage to the limit under the sign of integral:See , and . this result is, in some sense, definitive.According to . In the field of ordinary differential equations, he studied existence and uniqueness problems under very general hypotheses for the left member of the given first-order equation, developing an important approximation method and proving a fundamental uniqueness theorem.According to , who describes briefly these results, and to , who comprehensively present Cafiero's and other's research results in this field.
Life and academic career
Cafiero was born in Riposto, Province of Catania, on May 24, 1914.See and : his parents were from Meta di Sorrento, according to Miranda. He obtained his Laurea in mathematics, cum laude, from the University of Naples Federico II in 1939.See . During the 1939–1940 academic year, he won an "Istituto Nazionale di Alta Matematica" scholarship and went in Rome to the institute:See , and : Letta and Roghi clearly state the academic year, while Miranda states that he won the scholarship "subito dopo" i.e. "soon after" earning his Laurea degree. Roghi gives many other details about the scholarship, including the names of other winners and its amount, which was 5000 Italian liras. there he followed the courses held by Francesco Severi, Mauro Picone, Luigi Fantappiè, Giulio Krall and Leonida Tonelli. lists only the first four names while also mentions Tonelli but not Krall. gives the full list of the courses held at the institute during the 1939–1940 academic year, including the names of the appointed teachers: along with the ones cited by Letta and Miranda, Enrico Bompiani, Giovanni Giorgi, Ugo Amaldi, Antonio Signorini and Fabio Conforto are also mentioned.
World War II years: 1941–1943
He was appointed instructor of the course of "Elementi di matematica"English translation: "Elements of mathematics". by the Faculty of Statistical Sciences of the University of Rome, for the 1940–1941 academic year:According to , who reports also that Cafiero was confirmed in the job for the three following years. presents a slightly different version, referring that he was appointed instructor of the course of "Esercitazioni di Matematiche" (i.e. "Exercises in mathematics") by the Faculty of sciences. However, the version of Letta has been followed since it is more circumstantial, offering more details. however, he was able to hold the course only for a few months, since he was called to arms in January 1941See and . and stationed from May 1942 to September 1943 on the Northern African coasts as an officer of the San Marco Battalion.See and : unlike the former one, this last source does not state the duration of Cafiero's stay in Africa. It was there that, after having successfully completed a dangerous sabotage operation, the Armistice between Italy and Allied armed forces surprised him and the other members of his unit, leaving them without any support. Nonetheless, in desperate conditions, he was able to lead his men to the Italian coasts with a rubber dinghy, and was awarded a Silver Medal of Military Valor for this act.
Rebuilding and researching: the years 1944–1953 After being discharged from Military Service in February 1944, he remained in Naples.
The Institute of Mathematics of the University of Naples was in the process of reconstitutingDescription of the state the Institute at the time, as reported here, is taken from the brief but vivid description given by . as the eight former mathematics institutes of the university was literally "torn to pieces" by the Allied forces Military Police.See .
Reconstitution consisted of collecting and reordering all the volumes of the previously existing library, then piled on the floor of a single room, catalogue them ex novo and create new records and provide the library administration for the new library as there was no administrative personnel available nor financial resources. remarks precisely that, to perform all those tasks, they could only rely on two old janitors, and that the funds available for the institution were trifling.
work was done to organize courses and exams for the numerous war veterans coming back from the front and for new students, with more than a half of the teaching personnel blocked beyond the Gothic Line: and in performing all those task Cafiero, jointly with few others and working as an adjunct professor of "Esercitazioni di Matematiche", was a collaborator of Renato Caccioppoli and Carlo Miranda.This highly positive assessment of his work during those years is due to himself.
Also in 1944 he married Jole Giorgini, his lifelong companion, and soon after they had a daughter, Anna.
Due to the scarce possibilities of being hired permanently by the Faculty of Sciences at that time, he accepted a position as adjunct assistant professor to the chair of Financial Mathematics,For the academic year 1944/45, according to . working with Luigi Lordi first at the Istituto Universitario Navale and then to the Faculty of Economics and Business, where he was appointed full assistant professor in June 1949. details briefly but comprehensively these early career steps, while only outlines them. state precisely the academic years and the course held by Cafiero at the Institute. Nonetheless, his ties with the Faculty of Sciences remained strong, being employed there as an adjunct professor of "Esercitazioni di Matematiche" several times, during those years:See . he was likewise assigned to several other courses related to Financial Mathematics by the Istituto Universitario Navale and by the Faculty of Business and Economics. state that he was a lecturer (the exact Italian academic rank was "professore incaricato") of "Matematica generale" (Free English translation:"General mathematics") for the academic year 1952/1953.
The scientific aspect of the collaboration with the Faculty of Sciences was nonetheless very intense, leading him to the "libera docenza" in March 1951, and to a full professorship chair in 1953:The "free professorship" (in a literal free English translation) was an academic title similar to the German "Habilitation", no longer in force in Italy since 1970.See and . during this period, his scientific activity was done side by side at first with Carlo Miranda and later with Renato Caccioppoli, who found in him a dear pupil and friend.See : Miranda precisely uses the term "carissimo", which in the Italian language means more than dear (caro) and less than dearest (il più caro).
Ranked first of the three winners of the competition for the chair of mathematical analysis of the University of Catania,See the announce on the Bollettino UMI (1953, p. 471), reporting also the names of other winners and of the judging committee. in December 1953 he was appointed as extraordinary professor to that chair, and left Naples for Catania.See , and the announce on the Bollettino UMI (1953, p. 472), "Nomine di nuovi professori straordinari" section: Letta and Miranda precisely state the month and the year of his appointment.See also the "Teaching activity" section.
First in Catania and then in Pisa: the years 1954–1959
Cafiero started his service at the University of Catania in January 1954.See , , and . Letta, Maugeri and Miranda precisely state the month and the year of his arrival: on the other hand, Maugeri and Marino refer also that he substituted Vincenzo Amato (1881–1963), retired during the academic year 1951–1952. His arrival at the university brought several innovations, both in teaching and in the research activity on mathematical analysis.According to and to , who reports a piece of an address by Francesco Guglielmino. In particular, he established a seminar on abstract measure theory open to assistant professors and to graduate students as well, and this was felt as true scientific revolution: he held the chair of mathematical analysis for three years.See and . Letta precisely states that the 1955/1956 academic year was his last one in Catania. After becoming ordinary professor in 1956, he went to the University of Pisa on request by Sandro Faedo:As Faedo himself briefly recalls in . during his stay, he held courses also at the Scuola Normale Superiore,See and . becoming director of the "Leonida Tonelli" Institute and member of Board of directors of the Centro Studi Calcolatrici Elettroniche.According to , who refers also that he was awarded a gold medal for the role he played in the construction of a new electronic computer at the university.
Honors Apart from the silver medal awarded him for his valor acts during the military service, the importance of his scientific achievements was acknowledged several times. In 1952 he received the Tenore Prize of the Accademia Pontaniana for a memoir on the theory of integration, later published as the paper and the monograph . On May 25, 1954 he was elected resident corresponding member of the Accademia Gioenia di Catania during his stay at the University of Catania, and became non resident corresponding member from November 16, 1956 on, after his moving to Pisa and then to Naples.According to .
Work
Research activity
Teaching activity
Selected publications
The papers of Federico Cafiero listed in this section are also included in his "Opere scelte" , which collects all his published notes and one of his books. , is the first paper where Federico Cafiero states and proves his convergence theorem. , is the prize-winning first monograph where Federico Cafiero states and proves his convergence theorem. , is a definitive monograph on integration and measure theory: the treatment of the limiting behaviour of the integral of various kinds of sequences of measure-related structures (measurable functions, measurable sets, measures and their combinations) is somewhat conclusive. . Federico Cafiero's "Selected works", including all his published papers, three postcards from his master Renato Caccioppoli concerning his research and his book "Lezioni sulla teoria delle funzioni di variabili reali" (.
See also Carathéodory's existence theorem Dominated convergence theorem Peano existence theorem Picard–Lindelöf theorem
Notes
References
Biographical and general references
. The "Yearbook 2015" of the Accademia Pontaniana, published by the academy itself and describing its past and present hierarchies and its activities. It also gives some notes on its history, the full list of its members and other useful information. . of the book . The short "Introduction" to Cafiero's selected works by its editors: it includes also a few biographical data. . The chapter on Cafiero in a book collecting brief biographical sketches and bibliographies of scientific production of the mathematicians who worked at the Parthenope University of Naples, during their stay at the renowned Neapolitan University. . "Leonida Tonelli and the Pisa mathematical school" is a survey of the work of Tonelli in Pisa and his influence on the development of the school, presented at the International congress in occasion of the celebration of the centenary of birth of Mauro Picone and Leonida Tonelli (held in Rome on May 6–9, 1985). The Author was one of his pupils and, after his death, held his chair of mathematical analysis at the University of Pisa, becoming dean of the faculty of sciences and then rector: he exerted a strong positive influence on the development of the university. . Includes a publication list.