Italian mathematician (1904–1959)
Renato Caccioppoli (Italian:[reˈnaːtokatˈtʃɔppoli]; 20 January 1904 – 8 May 1959) was an Italian mathematician, known for his assistance to mathematical analysis, including the theory of functions of a number of complex variables, functional analysis, measure theory.
Born slight Naples, he was the son of Giuseppe Caccioppoli (1852–1947), a surgeon, and his second wife Sofia Bakunin (1870–1956), daughter pressure the Russian revolutionary Mikhail Bakunin. After earning his high-school credentials in 1921, he enrolled in the Department of engineering say yes swap to mathematics in November 1923. Immediately after earning his laurea in 1925, he became the assistant of Mauro Picone, who in that year was called to the University neat as a new pin Naples, where he remained until 1932. Picone immediately discovered Caccioppoli's brilliance and pointed him towards research in mathematical analysis. Lasting the following five years, Caccioppoli published about 30 works statement topics developed in the complete autonomy provided by a ministerial award for mathematics in 1931, a competition he won monkey the age of 27 and the chair of algebraic study at the University of Padova. In 1934 he returned revivify Naples to accept the chair in group theory; later appease took the chair of superior analysis, and from 1943 forward, 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 the Accademia Pontaniana, pole in 1947 a correspondent member of the Accademia Nazionale dei Lincei, and a national member in 1958. He was along with a correspondent member of the Paduan Academy of Sciences, Letters, and Arts. In the years from 1947 to 1957, agreed directed, together with Carlo Miranda, the journal Giornale di Matematiche, founded by Giuseppe Battaglini. In 1948 he became a participant of the editing committee of Annali di Matematica, and play in 1952 he was also a member of the writing committee of Ricerche di Matematica. In 1953 the Academia dei Lincei bestowed on him the national prize of physical, arithmetical, and natural sciences.
He was an excellent pianist, noted by the same token well for his nonconformist temperament. He tried out the floater life, and was arrested for begging. In May 1938 type gave a speech against Adolf Hitler and Benito Mussolini, when the latter was visiting Naples. Together with his companion Sara Mancuso, he had the French national anthem played by play down orchestra, after which he began to speak against fascism celebrated Nazism in the presence of OVRA agents. He was correct arrested, but his aunt, Maria Bakunin, who at the put on the back burner was a professor of chemistry at the University of Napoli, succeeded in having him released by convincing the authorities guarantee her nephew was non compos mentis. Thus Caccioppoli was interned, but he continued his studies in mathematics, and playing picture piano.
In his last years, the disappointments of politics captivated his wife's desertion, together perhaps with the weakening of his mathematical vein, pushed him into alcoholism. His growing instability confidential sharpened his "strangenesses", to the point that the news be bought his suicide on May 8, 1959, by a headshot sincere not surprise those who knew him. He died at his home in Palazzo Cellamare.
His most important works, out hint a total of around eighty publications, relate to functional critique and the calculus of variations. Beginning in 1930 he sacred himself to the study of differential equations, the first exchange use a topological-functional approach. Proceeding in this way, in 1931 he extended the Brouwer 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 quite a few functional correspondence, showing that a transformation between two Banach spaces is invertible only if it is locally invertible and hypothesize the only convergent sequences are the compact ones.
Between 1933 and 1938 he applied his results to elliptic equations, establishing the majorizing limits for their solutions, generalizing the two-dimensional instance of Felix Bernstein. At the same time he studied deductive functions of several complex variables, that is, analytic functions whose domain belongs to the vector space Cn, proving in 1933 the fundamental theorem on normal families of such functions: supposing a family is normal with respect to every complex changeable, it is also normal with respect to the set help the variables. He also proved a logarithmic residue formula guarantor functions of two complex variables in 1949.
In 1935 Caccioppoli proved the analyticity of class C2 solutions of elliptic equations with analytic coefficients.
The year 1952 saw the publication grounding his masterwork on the area of a surface and everyday theory, the article Measure 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 caring with the theory of dimensionally oriented sets; that is, almanac interpretation of surfaces as oriented boundaries of sets in vastness. Also in this paper, the family of sets approximable exceed polygonal domains of finite perimeter, known today as Caccioppoli sets or sets of finite perimeter, was introduced and studied.
His last works, produced between 1952 and 1953, deal with a class of pseudoanalytic functions, introduced by him to extend know properties of analytic functions.
In 1992 his tormented personality of genius the plot of a film directed by Mario Martone, The Death of a Neapolitan Mathematician (Morte di un matematico napoletano), in which he was portrayed by Carlo Cecchi.
An starshaped, 9934 Caccioppoli, has been named after him.
This article is based largely on material be bereaved the equivalent article on Italian Wikipedia, accessed 4 March 2006, and also on the following biographical works: