Federico Cafiero

Federico Cafiero
Born(1914-05-24)24 May 1914
Riposto
Died7 May 1980(1980-05-07) (aged 65)
Napoli
NationalityItalian
Alma materUniversità degli Studi di Napoli Federico II
Awards
Scientific career
Fields
Institutions
Doctoral advisorRenato Caccioppoli

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:[3] this result is, in some sense, definitive.[4] 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.[5]

  1. ^ Awarded for the monograph (Cafiero 1953a), according to (De Angelis & Sbordone 1999, p. 29), (de Lucia & Sbordone 1996), (Letta 1981, p. 347) and (Miranda 1980–1981, p. 9). The yearbook of the Accademia Pontaniana (2015, p. 123), in the list of prize recipients, states that the award winning memoir title was:-"Studio delle famiglie di funzioni additive di insieme; esposizione sistematica di risultati recenti e nuovi contributi; applicazioni alla teoria generale del passaggio al limite sotto il segno di integrale".
  2. ^ See the list of prize winners at the Presidenza della Repubblica Italiana web site.
  3. ^ See (Cafiero 1953), (Cafiero 1953a) and (Cafiero 1959, pp. 388–392).
  4. ^ According to Letta (1981, pp. 353–354).
  5. ^ According to Letta (1981, pp. 349–350), who describes briefly these results, and to Piccinini, Stampacchia & Vidossich (1978), who comprehensively present Cafiero's and other's research results in this field.