Luigi Amerio

Luigi Amerio
Born	August 15, 1912 Padova
Died	September 28, 2004 (aged 92) Milano
Nationality	Italian
Fields	Almost periodic functions Laplace transform Elliptic partial differential equations Hyperbolic partial differential equationss
Institutions	University of Genova Polytechnic University of Milan
Alma mater	Polytechnic University of Milan
Doctoral advisor	Mauro Picone

Luigi Amerio (15 August 1912 – 28 September 2004), was an Italian electrical engineer and mathematician. He is known for his work on almost periodic functions, on Laplace transforms in one and several dimensions, and on the theory of elliptic partial differential equations.

Works

A selection of Luigi Amerio's scientific papers is published in the two volumes of his "Selecta" (Amerio 1990): he is also the author of several university textbooks and, jointly with his pupil Giovanni Prouse, he wrote the influential monograph on almost periodic functions (Amerio & Prouse 1971).

• Amerio, Luigi (1943), "Su alcune questioni relative alla trasformazione di Laplace", Istituto Lombardo di Scienze e Lettere, Rendiconti, Classe di Scienze Matematiche e Naturali, Serie III (in Italian) 76 (7): 191–216, MR 0011501, Zbl 0060.24909. In the paper "On some questions related to the Laplace transform" (English translation of title), Luigi Amerio proves an important theorem on Laplace transform.
• Amerio, Luigi (1945), "Sull'integrazione delle equazioni lineari a derivate parziali del secondo ordine di tipo ellittico" (PDF), Acta. Pontificia Academia Scientarum 9: 213–228, MR 0025665, Zbl 0061.22502. "On the integration of linear elliptic second order partial differential equations" (English translation of the title) is a research announcement disclosing the results published in (Amerio 1945) and (Amerio 1947).
• Amerio, Luigi (1945), "Sull'integrazione dell'equazione Δ₂u - u = f in un dominio di connessione qualsiasi", Istituto Lombardo di Scienze e Lettere, Rendiconti, Classe di Scienze Matematiche e Naturali, Serie III (in Italian) 78 (9): 79–102, MR 0021206, Zbl 0061.23703. In the paper "On the integration of the equation Δ₂u - u = f on a domain with any connection" (English translation of the title), Amerio obtained the first theoretical results on Mauro Picone's method of solving boundary value problems for elliptic partial differential equations by the Riesz-Fischer theorem.
• Amerio, Luigi (July 1947), "Sul Calcolo delle Soluzioni dei Problemi al Contorno per le Equazioni Lineari del Secondo Ordine", American Journal of Mathematics (in Italian) 69 (3): 447–489, doi:10.2307/2371879, JSTOR 2371879, MR 0021207, Zbl 0034.20202. In the paper "On the calculus of solutions to boundary problems for linear second order equations" (English translation of the title), Luigi Amerio continues the studies initiated in (Amerio 1945).
• Amerio, Luigi; Prouse, Giovanni (1971), Almost-periodic functions and functional equations, The University Series in Higher Mathematics, New York–Cincinnati–Toronto–London–Melbourne: Van Nostrand Reinhold, pp. viii+184, ISBN 0-442-20295-4, MR 275061, Zbl 0215.15701.
• Amerio, Luigi (1990), Selecta, Milano: CUSL, pp. 520 (Volume I), pp. 521–1036 (Volume II). Luigi Amerio's "Selecta" in two volumes, collecting a selection of his scientific contributions.

Addresses, biographical and survey papers

• Amerio, Luigi; Cinquini, Silvio; Ghizzetti, Aldo (1948), Analisi matematica in Italia nel campo reale (dal 1939 al 1945), Pontificiae Academiae Scientiarum, Relationes de auctis scientiis tempore Belli (in Italian), n. 22, pp. 1–85, MR 0031525. "Mathematical analysis in Italy in the real field (from 1939 to 1945)" is an ample survey on the research results in mathematical analysis, including the theory of integral equations and the theory of ordinary and partial differential equations, obtained by Italian mathematicians during the Second world war, published by the Pontificial Academy of Sciences.
• Amerio, Luigi (1986), "Indirizzo di adesione", in Montalenti, G.; Amerio, L.; Acquaro, G.; Baiada, E.; et al., Convegno celebrativo del centenario della nascita di Mauro Picone e Leonida Tonelli (6–9 maggio 1985), Atti dei Convegni Lincei (in Italian) 77, Roma: Accademia Nazionale dei Lincei, p. 9. The brief "participating address" presented to the International congress on the occasion of the celebration of the centenary of birth of Mauro Picone and Leonida Tonelli (held in Rome on May 6–9, 1985) by Luigi Amerio on behalf of the Accademia Nazionale delle Scienze detta dei XL an of the Istituto Lombardo di Scienze e Lettere.
• Amerio, Luigi (1997), "Intervento", Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento, Serie IX, 8 (1): 15–16. The "Address" (free English translation) of Amerio at the meeting "Ricordo di Gaetano Fichera" (English translation: "Remembrance of Gaetano Fichera") held in Rome at the Accademia Nazionale dei Lincei on the 8th of February 1997.

See also

• Gaetano Fichera
• Analytic continuation
• Boundary value problem

References

Biographical and general references

• Citrini, Claudio (April 2001), "Intervista a Luigi Amerio", Bollettino della Unione Matematica Italiana, Sezione A, La Matematica nella Società e nella Cultura, Serie VIII (in Italian) IV (1): 11–32, MR 1885104, Zbl 1194.01080. "Interview with Luigi Amerio" is the published transcription of an ample interview by Claudio Citrini, one of Amerio's pupils and collaborators.
• Citrini, Claudio (27 October 2011), "Luigi Amerio, maestro di scienza e di vita" (PDF), La Matematica Applicabile. Giornata di Studio in memoria di Luigi Amerio (PDF) (in Italian), Milano: Istituto Lombardo di Scienze e Lettere, p. 12. "Luigi Amerio, master in science and life" is the commemorative speech pronounced by Claudio Citrini, on the occasion of the meeting "Applicable Mathematics. Day seminar in memory of Luigi Amerio".
• Prouse, Giovanni (December 2006), "Commemorazione di Luigi Amerio" (PDF), Bollettino della Unione Matematica Italiana, Sezione A, La Matematica nella Società e nella Cultura, Serie VIII (in Italian) IX (1): 533–544, MR 2309900, Zbl 1195.01077. "Commemoration of Luigi Amerio" is a biographical paper written by Giovanni Prouse, pupil and collaborator of Amerio.

Scientific references

• Fichera, Gaetano (1950), "Risultati concernenti la risoluzione delle equazioni funzionali lineari dovuti all'Istituto Nazionale per le applicazioni del calcolo", Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali, Serie VIII (in Italian) 3 (1): 1–81, MR 0036409, Zbl 0066.09902. "Results concerning the solutions of linear functional equations due to the National Institute for Calculus Applications" (English translation of the title) is 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 using the methods of functional analysis.
• Ghizzetti, Aldo (1945), Analisi matematica in Italia nel campo complesso (dal 1939 al 1945), Pontificiae Academiae Scientiarum, Relationes de auctis scientiis tempore Belli (in Italian) n. 5, pp. 1–35, MR 0024969, Zbl 0061.14204. "Mathematical analysis in Italy in the complex field (from 1939 to 1945)" is a survey on the research results in complex analysis, including the theory of functions of several complex variables and the theory of analytic functionals, obtained by Italian mathematicians during the Second world war, published by the Pontificial Academy of Sciences.
• Miranda, Carlo (1955), Equazioni alle derivate parziali di tipo ellittico, Ergebnisse der Mathematik und ihrer Grenzgebiete – Neue Folge (in Italian), 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, Band 2 (2nd Revised ed.), Berlin – Heidelberg – New York: Springer Verlag, pp. XII+370, ISBN 978-3-540-04804-6, MR 0284700, Zbl 0198.14101, translated from the Italian by Zane C. Motteler.