Carlo Miranda

Carlo Miranda (15 August 1912 – 28 May 1982) was an Italian mathematician, working on mathematical analysis, theory of elliptic partial differential equations and complex analysis: he is known for giving the first proof of the Poincaré–Miranda theorem,^[1] for Miranda's theorem in complex analysis,^[2] and for writing an influential monograph in the theory of elliptic partial differential equations.^[3]

Carlo Miranda
Born	(1912-08-15)15 August 1912 Naples
Died	28 May 1982(1982-05-28) (aged 69) Naples
Nationality	Italian
Known for	Poincaré–Miranda theorem Miranda's theorem Theory of elliptic partial differential equations
Scientific career
Fields	Mathematical analysis Complex analysis Theory of elliptic partial differential equations
Institutions	University of Genoa Polytechnic University of Turin University of Naples Federico II
Doctoral advisor	Mauro Picone

Selected works

Scientific works

Articles

• Miranda, Carlo (27 May 1935), "Un nouveau critère de normalité pour les familles de fonctions holomorphes" [A new normality criterion for families of holomorphic functions], Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), 200: 1823, ISSN 0001-4036, JFM 61.1154.05, Zbl 0011.31102, available at Gallica.
• Miranda, Carlo (1935a), "Sur un nouveau critère de normalité pour les familles de fonctions holomorphes" [On a new normality criterion for families of holomorphic functions], Bulletin de la Société Mathématique de France (in French), 63: 185–196, doi:10.24033/bsmf.1231, ISSN 0037-9484, JFM 61.1155.01, Zbl 0013.27202, available at NUMDAM.
• Miranda, Carlo (1940), "Un'osservazione su un teorema di Brouwer" [An observation on a theorem of Brouwer], Bollettino dell'Unione Matematica Italiana, Serie 2 (in Italian), 3: 5–7, ISSN 0041-7084, JFM 66.0217.01, MR 0004775, Zbl 0024.02203.

Books

• Miranda, Carlo (1949), Problemi di esistenza in analisi funzionale [Existence problems in functional analysis], Quaderni (in Italian), vol. 3, Pisa: Litografia Tacchi on behalf of Scuola Normale Superiore, p. ii+184, MR 0037461, Zbl 0041.43401.
• Miranda, Carlo (1955), Equazioni alle derivate parziali di tipo ellittico, Ergebnisse der Mathematik und ihrer Grenzgebiete – Neue Folge (in Italian), vol. Heft 2 (1st ed.), Berlin – Göttingen – New York: Springer Verlag, pp. VIII+222, MR 0087853, Zbl 0065.08503.
• Miranda, Carlo (1970) [1955], Partial Differential Equations of Elliptic Type, Ergebnisse der Mathematik und ihrer Grenzgebiete – 2 Folge, vol. Band 2, translated by Motteler, Zane C. (2nd Revised ed.), Berlin – Heidelberg – New York: Springer Verlag, pp. XII+370, doi:10.1007/978-3-642-87773-5, ISBN 978-3-540-04804-6, MR 0284700, Zbl 0198.14101.
• Miranda, Carlo (1972), Su alcuni problemi di geometria differenziale in grande per gli ovaloidi [On some problems of differential geometry in the large concernig ovaloids], Quaderni (in Italian), Pisa: Edizioni della Normale, p. ii+123, MR 0467615, Zbl 0338.53044.
• Miranda, Carlo (1978), Istituzioni di analisi funzionale lineare [Foundations of linear functional analysis], Monografie Matematiche (in Italian), Bologna: Unione Matematica Italiana, pp. (Vol. I) VIII+596, (Vol. II) 152, Zbl 0697.46001 (and Zbl 0697.46002 for the second volume).
• Miranda, Carlo (1992), Opere scelte [Selected works] (in Italian and French), Firenze: Edizioni Cremonese (distributed by Unione Matematica Italiana), pp. XXIV+516 (vol. 1), pp. VIII+517–1066 (vol. 2), ISBN 88-7083-719-X: two volumes collecting his most important mathematical papers in their original language and typographical form, and a full list of Miranda's publications.

Commemorative, historical, and survey works

• Miranda, Carlo (July–December 1950), "Risultati concernenti la risoluzione delle equazioni funzionali lineari dovuti all'Istituto Nazionale per le Applicazioni del Calcolo" [Results regarding the solution of linear functional equations due to the National Institute for Calculus Applications], Rendiconti di Matematica e delle sue Applicazioni, 5 (in Italian), 9 (3–4): 346–353, ISSN 0034-4427, MR 0041759, Zbl 0040.35304. This work completes a survey of Fichera (1950) with the same title, by elucidating the role of some scientists and adding a further bibliography.
• Miranda, Carlo (1978), "Breve storia e prospettive future dell'istituto di matematica della facolta di scienze dell'universita di Napoli" [Brief history and future perspectives of the institute of mathematics of the faculty of science of the University of Naples], Rendiconto dell'Accademia delle Scienze Fisiche e Matematiche, Napoli, Serie IV (in Italian), 44 (1977): 7–44, ISSN 0370-3568, MR 0497758, Zbl 0384.01020.
• Miranda, Carlo (1980–1981), "Federico Cafiero", Rendiconto dell'Accademia delle Scienze Fisiche e Matematiche, Napoli, Serie IV (in Italian), 48: 9–16, ISSN 0370-3568, MR 0697874, Zbl 0512.01007.

See also

• Luigi Amerio
• Schottky's theorem
• Singular integral

Notes

1. (Kulpa 1997, p. 545).
2. (Burckel 1979, p. 426, pp. 436–437, and pp. 456–457).
3. See (Miranda 1955) and its revised and translated second edition (Miranda 1970).

References

Biographical references

• Accademia Nazionale dei Lincei (2012), (PDF) (in Italian), Roma: Accademia Nazionale dei Lincei, p. 734, archived from the original (PDF) on 2016-03-04, retrieved 2016-04-17. The "Yearbook" of the renowned Italian scientific institution, including an historical sketch of its history, the list of all past and present members as well as a wealth of informations about its academic and scientific activities.
• Accademia Pontaniana (2015), (PDF) (in Italian), Napoli: Nella Sede dell'Accademia, p. 180, archived from the original (PDF) on 2015-03-06, retrieved 2016-03-28. 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.
• Greco, Donato (1983), "Intervento di Donato Greco all'apertura del Convegno", in Greco, Donato (ed.), Methods of Functional Analysis and Theory of Elliptic Equations. Proceedings of the international meeting dedicated to the memory of professor Carlo Miranda. Naples, September 13–16, 1982 (in Italian), Napoli: Istituto di Matematica "R. Caccioppoli" dell'Università di Napoli – Liguori Editore, pp. 9–10, MR 0819004, Zbl 0583.00017
• Ciliberto, Carlo (1983), "Intervento di Carlo ciliberto, Rettore dell'Università di Napoli", in Greco, Donato (ed.), Methods of Functional Analysis and Theory of Elliptic Equations. Proceedings of the international meeting dedicated to the memory of professor Carlo Miranda. Naples, September 13–16, 1982 (in Italian), Napoli: Istituto di Matematica "R. Caccioppoli" dell'Università di Napoli – Liguori Editore, pp. 11–14, MR 0819004, Zbl 0583.00017
• Scorza Dragoni, Giuseppe (1983), "Intervento di Giuseppe Scorza Dragoni", in Greco, Donato (ed.), Methods of Functional Analysis and Theory of Elliptic Equations. Proceedings of the international meeting dedicated to the memory of professor Carlo Miranda. Naples, September 13–16, 1982 (in Italian), Napoli: Istituto di Matematica "R. Caccioppoli" dell'Università di Napoli – Liguori Editore, pp. 15–17, MR 0819004, Zbl 0583.00017.
• Scorza Dragoni, Giuseppe (1984), "Ricordo di Carlo Miranda" [Recollection of Carlo Miranda], Rendiconti della Accademia Nazionale delle Scienze Detta dei XL. Memorie di Matematica e Applicazioni, Serie V, Roma, VIII (13): 275–278, ISSN 0392-4106, MR 0774923, Zbl 0556.01017. An almost identical transcription of the commemoration (Scorza Dragoni 1983), published on the journal of the Academia for the wish of Givanni Battista Marini Bettolo to honor Carlo Miranda for his important work for the journal itself.
• Società Nazionale di Scienze Lettere e Arti in Napoli (2014), (PDF) (in Italian), Napoli: Società Nazionale di Scienze Lettere e Arti in Napoli, p. 82, archived from the original (PDF) on 2016-03-03, retrieved 2016-03-28. The "Yearbook 2014" of the Società Nazionale di Scienze Lettere e Arti in Napoli, published by the society itself and describing its past and present hierarchies, and its activities. It also reports some notes on its history, the full list of its members and other useful information.

General references

• Avantaggiati, Antonio (1985), "Carlo Miranda", Bollettino dell'Unione Matematica Italiana, Serie IV, A (in Italian), 11 (1): 137–153, ISSN 0392-4033, MR 0781807, Zbl 0556.01016: includes a list of Miranda's publications.
• Cecconi, Jaurés Pacifico (1984), "Carlo Miranda", Atti della Accademia Ligure di Scienze e Lettere, Serie V (in Italian), XL: 45–48, ISSN 0365-0278, MR 0825356.
• Geymonat, Giuseppe (1985), "Carlo Miranda", Atti della Accademia delle Scienze di Torino – Classe di Scienze Fisiche, Matematiche e Naturali (in Italian), 119 (5–6): 292–295, ISSN 0001-4419, MR 0929908, Zbl 1200.01014.
• Greco, Donato (1985), Carlo Miranda, Profili e Ricordi (in Italian), vol. 12, Napoli: Società Nazionale di Scienze Lettere e Arti in Napoli, p. 31: includes a list of Miranda's publications.
• Magenes, Enrico (1983), "Carlo Miranda", Annali di Matematica Pura ed Applicata, Serie IV (in Italian), 27 (1–2): I–III, doi:10.1007/BF01781059, ISSN 0373-3114, MR 0750524, S2CID 186222655, Zbl 0536.01031.

Scientific references

• Burckel, Robert B. (1979), An Introduction to Classical Complex Analysis. Vol. 1, Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften. Mathematische Reihe, vol. Band 64, Basel–Stuttgart: Birkhäuser Verlag, p. 570, ISBN 3-7643-0989-X, MR 0555733, Zbl 0434.30001.
• Cimmino, Gianfranco; Scorza Dragoni, Giuseppe (1984), "L'opera Matematica di Carlo Miranda" [The mathematical work of Carlo Miranda], Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali, Series VIII (in Italian), LXXVI (2): 145–157, ISSN 0392-7881, MR 0814350: includes a list of Miranda's publications.
• Dugundji, James; Granas, Andrzej (2003), Fixed Point Theory, Springer Monographs in Mathematics, New York: Springer-Verlag, pp. xv+690, doi:10.1007/978-0-387-21593-8, ISBN 0-387-00173-5, MR 1987179, Zbl 1025.47002.
• Fichera, Gaetano (1950), "Risultati concernenti la risoluzione delle equazioni funzionali lineari dovuti all'Istituto Nazionale per le applicazioni del calcolo" [Results concerning the solutions of linear functional equations due to the National Institute for Calculus Applications], Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali, Serie VIII (in Italian), 3 (1): 1–81, ISSN 0365-0286, MR 0036409, Zbl 0066.09902. An ample survey paper on results on the solutions of linear integral and partial differential equation obtained by the research team of Mauro Picone at the Istituto Nazionale per le Applicazioni del Calcolo, by using methods from functional analysis.
• Kulpa, Wladyslaw (June 1997), "The Poincare-Miranda Theorem", The American Mathematical Monthly, 104 (6): 545–550, doi:10.2307/2975081, JSTOR 2975081, MR 1453657, Zbl 0891.47040.
• Lanconelli, Ermanno; Sbordone, Carlo; Spagnolo, Sergio; Trombetti, Guido (1992), "Introduzione", in Miranda, Carlo (ed.), Opere scelte (in Italian), Firenze: Edizioni Cremonese (distributed by Unione Matematica Italiana), pp. XI–XVI (of vol. 1). The "Introduction" to his "Selected works" by the members of the UMI scientific commission who edited them.

Publications dedicated to his memory

• Greco, Donato, ed. (1983), Methods of Functional Analysis and Theory of Elliptic Equations. Proceedings of the international meeting dedicated to the memory of professor Carlo Miranda. Naples, September 13–16, 1982 (in English, French, and Italian), Napoli: Istituto di Matematica "R. Caccioppoli" dell'Università di Napoli – Liguori Editore, p. 362, MR 0819004, Zbl 0583.00017

External links

• O'Connor, John J.; Robertson, Edmund F. (July 2012), "Carlo Miranda", MacTutor History of Mathematics Archive, University of St Andrews