Renato Caccioppoli | |
|---|---|
 | |
| Born | (1904-01-20)20 January 1904 |
| Died | 8 May 1959(1959-05-08) (aged 55) |
| Alma mater | University of Naples Federico II |
| Known for | Caccioppoli set |
| Scientific career | |
| Fields | |
| Institutions | |
| Doctoral advisor | Mauro Picone |
| Doctoral students | |
Renato Caccioppoli (Italian:[reˈnaːtokatˈtʃɔppoli]; 20 January 1904 – 8 May 1959) was an Italianmathematician, known for his contributions tomathematical analysis, including thetheory of functions of several complex variables,functional analysis,measure theory.
Born inNaples, he was the son of Giuseppe Caccioppoli (1852–1947), asurgeon, and his second wife Sofia Bakunin (1870–1956), daughter of the Russian revolutionaryMikhail Bakunin. After earning his high-school diploma in 1921, he enrolled in the Department of engineering to swap to mathematics in November 1923. Immediately after earning hislaurea in 1925, he became the assistant ofMauro Picone, who in that year was called to theUniversity of Naples, where he remained until 1932. Picone immediately discovered Caccioppoli's brilliance and pointed him towards research inmathematical analysis. During the following five years, Caccioppoli published about 30 works on topics developed in the complete autonomy provided by a ministerial award for mathematics in 1931, a competition he won at the age of 27 and the chair ofalgebraic analysis at theUniversity of Padova. In 1934 he returned to Naples to accept the chair ingroup theory; later he took the chair of superior analysis, and from 1943 onwards, the chair in mathematical analysis.
In 1931 he became a correspondent member of the Academy of Physical and Mathematical Sciences of Naples, becoming an ordinary member in 1938. In 1944 he became an ordinary member of theAccademia Pontaniana, and in 1947 a correspondent member of theAccademia Nazionale dei Lincei, and a national member in 1958. He was also a correspondent member of thePaduan Academy of Sciences, Letters, and Arts. In the years from 1947 to 1957, he directed, together withCarlo Miranda, the journalGiornale di Matematiche, founded byGiuseppe Battaglini. In 1948 he became a member of the editing committee ofAnnali di Matematica, and starting in 1952 he was also a member of the editing committee ofRicerche di Matematica. In 1953 the Academia dei Lincei bestowed on him the national prize of physical, mathematical, and natural sciences.
He was an excellentpianist, noted as well for his nonconformist temperament. He tried out the vagrant life, and was arrested for begging. In May 1938 he gave a speech againstAdolf Hitler andBenito Mussolini, when the latter was visiting Naples. Together with his companion Sara Mancuso, he had the French nationalanthem played by an orchestra, after which he began to speak againstfascism andNazism in the presence ofOVRA agents. He was again arrested, but his aunt,Maria Bakunin, who at the time was a professor of chemistry at theUniversity of Naples, succeeded in having him released by convincing the authorities that her nephew wasnon compos mentis. Thus Caccioppoli was interned, but he continued his studies in mathematics, and playing the piano.
In his last years, the disappointments ofpolitics and his wife's desertion, together perhaps with the weakening of his mathematical vein, pushed him intoalcoholism. His growing instability had sharpened his "strangenesses", to the point that the news of his suicide on May 8, 1959, by a headshot did not surprise those who knew him. He died at his home inPalazzo Cellamare.
His most important works, out of a total of around eighty publications, relate tofunctional analysis and thecalculus of variations. Beginning in 1930 he dedicated himself to the study ofdifferential equations, the first to use a topological-functional approach. Proceeding in this way, in 1931 he extended theBrouwer fixed point theorem, applying the results obtained both from ordinary differential equations and partial differential equations.
In 1932 he introduced the general concept of inversion of functional correspondence, showing that a transformation between twoBanach spaces is invertible only if it is locally invertible and if the only convergent sequences are the compact ones.
Between 1933 and 1938 he applied his results toelliptic equations, establishing the majorizing limits for their solutions, generalizing the two-dimensional case ofFelix Bernstein. At the same time he studiedanalytic functions ofseveral complex variables, that is, analytic functions whosedomain belongs to the vector spaceCn, proving in 1933 the fundamental theorem on normal families of such functions: if a family is normal with respect to every complex variable, it is also normal with respect to the set of the variables. He also proved alogarithmic residue formula for functions of two complex variables in 1949.
In 1935 Caccioppoli proved the analyticity of classC2 solutions of elliptic equations with analytic coefficients.
The year 1952 saw the publication of his masterwork on the area of a surface andmeasure theory, the articleMeasure and integration of dimensionally oriented sets (Misura e integrazione degli insiemi dimensionalmente orientati, Rendiconti dell'Accademia Nazionale dei Lincei, s. VIII, v.12). The article is mainly concerned with the theory of dimensionally oriented sets; that is, an interpretation of surfaces as oriented boundaries of sets in space. Also in this paper, the family of sets approximable by polygonal domains of finite perimeter, known today asCaccioppoli sets orsets of finite perimeter, was introduced and studied.
His last works, produced between 1952 and 1953, deal with a class ofpseudoanalytic functions, introduced by him to extend certain properties ofanalytic functions.
In 1992 his tormented personality inspired the plot of a film directed byMario Martone,The Death of a Neapolitan Mathematician (Morte di un matematico napoletano), in which he was portrayed byCarlo Cecchi.
Anasteroid,9934 Caccioppoli, has been named after him.
This article is based largely on material fromthe equivalent article on Italian Wikipedia, accessed 4 March 2006, and also on the following biographical works:
{{citation}}:ISBN / Date incompatibility (help). The work of Cesari summarizing the theory of surface area, including his own contributions.