In the theory of functions of several complex variables he introduced the concept of pseudoconvexity[b] during his investigations on the domain of existence of such functions: it turned out to be one of the key concepts of the theory.
The full scientific production of Eugenio Elia Levi is collected in reference (Levi 1959–1960).
Levi, Eugenio Elia (2 April 1905), "Sulla struttura dei gruppi finiti e continui" [On the structure of finite simple groups], Atti della Reale Accademia delle Scienze di Torino. (in Italian), XL: 551–565, JFM 36.0217.02, reprinted also in Levi 1959–1960, pp. 101–126, volume I. A a well-known memoir in Group theory: it was presented to the members of the Accademia delle Scienze di Torino during the session of April 2, 1905, by Luigi Bianchi.
Levi, Eugenio Elia (1907a), "Sulle equazioni lineari alle derivate parziali totalmente ellittiche" [On linear totally elliptic partial differential equations], Rendiconti della Reale Accademia dei Lincei, Classe di Scienze Fisiche, Matematiche, Naturali, Serie V (in Italian), 16 (1): 932–938, JFM 38.0403.01. A short note announcing the results of paper (Levi 1907b).
Levi, Eugenio Elia (1907b), "Sulle equazioni lineari totalmente ellittiche alle derivate parziali" [On linear totally elliptic partial differential equations], Rendiconti del Circolo Matematico di Palermo (in Italian), 24 (1): 275–317, doi:10.1007/BF03015067, JFM 38.0402.01. An important paper whose results were previously announced in the short note (Levi 1907a) with the same title. It was also translated in Russian by N. D. Ajzenstat, currently available from the All-Russian Mathematical Portal: Levi, E. E. (1941), "On linear elliptic partial differential equations", Uspekhi Matematicheskikh Nauk (in Russian) (8): 249–292.
Levi, Eugenio Elia (1911), "Sulle ipersuperficie dello spazio a 4 dimensioni che possono essere frontiera del campo di esistenza di una funzione analitica di due variabili complesse" [On the hypersurfaces of the 4-dimensional space that can be the boundary of the domain of existence of an analytic function of two complex variables], Annali di Matematica Pura ed Applicata, s. III (in Italian), XVIII (1): 69–79, doi:10.1007/BF02420535, JFM 42.0449.02. Another important paper in the theory of functions of several complex variables, investigating further the theory started in (Levi 1910).
Levi, Eugenio Elia (1959–1960), Opere [Collected works] (in Italian), Roma: Edizioni Cremonese (distributed by Unione Matematica Italiana), pp. XX + 418 (Volume I), 448 (Volume II), MR 0123464, Zbl 0091.00108. His "Collected works" in two volumes, collecting all the mathematical papers of Eugenio Elia Levi in a revised typographical form, both amending typographical errors and author's oversights. A collection of all his published papers (in their original typographical form), probably an unordered uncorrected collection of offprints, is available online at the Internet Archive: Levi, Eugenio Elia, , Los Angeles: UCLA, p. 782, archived from the original on 9 August 2016.
^This section is mainly based on the survey article by Picone (1959) included in Levi's "Opere (Collected works)", describing his researches briefly but comprehensively; occasionally, also the comments of Guido Fubini in (Fubini & Loria 1918) are taken into account.
^See the two well known papers (Levi 1910) and (Levi 1910): Levi deals with functions of two complexvariables, but his calculations can be extended to functions with any finite number of variables, as he explicitly states. Levi, following a then well established practice, does not use Wirtinger derivatives.
References
Biographical and general references
Celli, Andrea; Mattaliano, Maurizio, eds. (2015), Eugenio Elia Levi, le speranze perdute della Matematica italiana (in Italian), Milano: EGEA, pp. LIV+326, ISBN978-88-2384-461-2. Wide source of unpublished manuscript documents of and about E.E. Levi. A short presentation could be found on EGEA website
Coen, Salvatore (1999), "Beppo Levi: una biografia", in Levi, Beppo (ed.), Opere. Volume I: 1897–1926 [Collected works. Volume I:1897–1926] (in Italian), Bologna: Edizioni Cremonese (distributed by Unione Matematica Italiana), pp. XIII–LIV, Zbl 1054.01520. An ample biographical paper (nearly 40 pages) on Beppo Levi: an earlier version of it was published as Coen, Salvatore (1994), "Beppo Levi: la vita", in Coen, Salvatore (ed.), Seminari di geometria, Università di Bologna, Italia, 1991–1993 (in Italian), Bologna: Università degli Studi di Bologna, Dipartimento di Matematica, pp. 193–232, MR 1265762, Zbl 0795.01022. It gives many useful information on the family and on the relationship between the two Levi brothers.
D'Ovidio, E.; Bianchi, L.; Volterra, V. (1912), [Report on the prize for Mathematics for the year 1912, presented by the Commission consisting of Members: D'Ovidio, Bianchi, Volterra], Rendiconti della Accademia Nazionale delle Scienze detta dei XL, Memorie di Matematica e Applicazioni, Serie 3 (in Italian), XVII (62): XXIV–XXV, archived from the original on 27 September 2011. The relation of Enrico D'Ovidio, Luigi Bianchi and Vito Volterra motivating their decision for the awarding of the golden medal of the Accademia Nazionale delle Scienze detta dei XL to Eugenio Elia Levi.
Fubini, Guido; Loria, Gino (1918), "Eugenio Elia Levi (1883–1917)", Bollettino di Bibliografia e Storia delle Scienze Matematiche (in Italian), 20: 38–45, JFM 46.0019.07. The most widely known biographical reference on Eugenio Elia Levi, written by Guido Fubini and Gino Loria.
Loria, Gino (1918), Panegirico di un Eroe. Commemorazione del Prof. Eugenio Elia Levi pronunziata nell'aula magna dell'Università di Genova addì XXIX maggio MCMXVIII [Panegyric of a Hero. Commemoration of Prof. Eugenio Elia Levi pronounced in the auditorium of the University of Genoa on 29 May 1918] (in Italian), Sestri Ponente: S. L. A. G. / Bruzzone e C., p. 31. A pamphlet containing the commemoration of Eugenio Elia Levi pronounced by Gino Loria at the University of Genova on May 29, 1918.
Padoa, Alessandro (December 1917), "Eugenio Elia Levi", Bollettino della Mathesis (in Italian), 9: 89–92.
Picone, Mauro (1959), "Sulla Vita e sulle Opere di Eugenio Elia Levi", in Levi, Eugenio Elia (ed.), Opere. Volume I [Collected Works] (in Italian), Roma: Edizioni Cremonese (distributed by Unione Matematica Italiana), pp. V–XV, MR 0123464, Zbl 0091.00108. A commemorative paper on Eugenio Elia Levi written by Mauro Picone and included in the first volume of his Opere (Levi 1959–1960).
Roero, C.S. (31 January 2005), (in Italian), archived from the original on 27 September 2011, retrieved 12 January 2010.
Tricomi, G. F. (1962), "Eugenio Elia Levi", Matematici italiani del primo secolo dello stato unitario [Italian mathematicians of the first century of the unitary state], Memorie dell'Accademia delle Scienze di Torino. Classe di Scienze fisiche matematiche e naturali, series IV (in Italian), vol. I, p. 120, Zbl 0132.24405. Available from the website of the . An ample historical paper written by Francesco Tricomi to commemorate all Italian mathematicians who worked during the first century of the Italian State.
Vitali, Giuseppe (December 1917), "Eugenio Elia Levi", Bollettino della Mathesis (in Italian), 9: 86–89.
External links
Comoglio, Mauro (4 November 2010), La guerra del '15–'18 termina il 4 Novembre. Un anno prima era morto Eugenio Elia Levi (in Italian), MATEpristem, retrieved 13 June 2011.
Dell'Aglio, L. (2005), "LEVI, Eugenio Elia", Enciclopedia Treccani, Dizionario Biografico degli Italiani (in Italian), vol. LXIV, retrieved 15 September 2011. The biographical entry about Eugenio Elia Levi in the "Dizionario Biografico degli Italiani (Biographical Dictionary of Italians)" section of the Enciclopedia Treccani.
Guerraggio, Angelo; Nastasi, Pietro; Tricomi, Francesco (2008–2010), "Eugenio Elia Levi (1883–1917)", Edizione Nazionale Mathematica Italiana (in Italian), Scuola Normale Superiore, retrieved 18 January 2011. Available from the Edizione Nazionale Mathematica Italiana.
eugenio, elia, levi, october, 1883, october, 1917, italian, mathematician, known, fundamental, contributions, group, theory, theory, partial, differential, operators, theory, functions, several, complex, variables, younger, brother, beppo, levi, killed, action. Eugenio Elia Levi 18 October 1883 28 October 1917 was an Italian mathematician known for his fundamental contributions in group theory in the theory of partial differential operators and in the theory of functions of several complex variables He was a younger brother of Beppo Levi and was killed in action during First World War Eugenio Elia LeviBorn 1883 10 18 18 October 1883Torino ItalyDied28 October 1917 1917 10 28 aged 34 Cormons ItalyNationalityItalianAlma materScuola Normale SuperioreKnown forLevi decomposition Levi form Parametrix PseudoconvexityAwardsLavagna prize 1904 Golden medal of the Accademia Nazionale delle Scienze detta dei XL 1911 Scientific careerFieldsGroup theory Several complex variables Partial differential operatorsInstitutionsScuola Normale Superiore University of Genoa Contents 1 Work 1 1 Research activity 1 1 1 Differential geometry 1 1 2 Group theory 1 1 3 Function theory 1 1 4 Cauchy and Goursat problems 1 1 5 Boundary value problems 1 1 6 Calculus of variations 2 Publications 3 See also 4 Notes 5 References 5 1 Biographical and general references 6 External linksWork EditThis section needs expansion You can help by adding to it February 2021 Research activity Edit He wrote 33 papers classified by his colleague and friend Mauro Picone a according to the scheme reproduced in this section Differential geometry Edit Group theory Edit He wrote only three papers in group theory in the first one Levi 1905 discovered what is now called Levi decomposition which was conjectured by Wilhelm Killing and proved by Elie Cartan in a special case Function theory Edit In the theory of functions of several complex variables he introduced the concept of pseudoconvexity b during his investigations on the domain of existence of such functions it turned out to be one of the key concepts of the theory Cauchy and Goursat problems Edit Boundary value problems Edit His researches in the theory of partial differential operators lead to the method of the parametrix which is basically a way to construct fundamental solutions for elliptic partial differential operators with variable coefficients the parametrix is widely used in the theory of pseudodifferential operators Calculus of variations EditPublications EditThe full scientific production of Eugenio Elia Levi is collected in reference Levi 1959 1960 Levi Eugenio Elia 2 April 1905 Sulla struttura dei gruppi finiti e continui On the structure of finite simple groups Atti della Reale Accademia delle Scienze di Torino in Italian XL 551 565 JFM 36 0217 02 reprinted also in Levi 1959 1960 pp 101 126 volume I A a well known memoir in Group theory it was presented to the members of the Accademia delle Scienze di Torino during the session of April 2 1905 by Luigi Bianchi Levi Eugenio Elia 1907a Sulle equazioni lineari alle derivate parziali totalmente ellittiche On linear totally elliptic partial differential equations Rendiconti della Reale Accademia dei Lincei Classe di Scienze Fisiche Matematiche Naturali Serie V in Italian 16 1 932 938 JFM 38 0403 01 A short note announcing the results of paper Levi 1907b Levi Eugenio Elia 1907b Sulle equazioni lineari totalmente ellittiche alle derivate parziali On linear totally elliptic partial differential equations Rendiconti del Circolo Matematico di Palermo in Italian 24 1 275 317 doi 10 1007 BF03015067 JFM 38 0402 01 An important paper whose results were previously announced in the short note Levi 1907a with the same title It was also translated in Russian by N D Ajzenstat currently available from the All Russian Mathematical Portal Levi E E 1941 On linear elliptic partial differential equations Uspekhi Matematicheskikh Nauk in Russian 8 249 292 Levi Eugenio Elia 1910 Studii sui punti singolari essenziali delle funzioni analitiche di due o piu variabili complesse Studies on essential singular points of analytic functions of two or more complex variables Annali di Matematica Pura ed Applicata s III in Italian XVII 1 61 87 doi 10 1007 BF02419336 JFM 41 0487 01 An important paper in the theory of functions of several complex variables where the problem of determining what kind of hypersurface can be the boundary of a domain of holomorphy Levi Eugenio Elia 1911 Sulle ipersuperficie dello spazio a 4 dimensioni che possono essere frontiera del campo di esistenza di una funzione analitica di due variabili complesse On the hypersurfaces of the 4 dimensional space that can be the boundary of the domain of existence of an analytic function of two complex variables Annali di Matematica Pura ed Applicata s III in Italian XVIII 1 69 79 doi 10 1007 BF02420535 JFM 42 0449 02 Another important paper in the theory of functions of several complex variables investigating further the theory started in Levi 1910 Levi Eugenio Elia 1959 1960 Opere Collected works in Italian Roma Edizioni Cremonese distributed by Unione Matematica Italiana pp XX 418 Volume I 448 Volume II MR 0123464 Zbl 0091 00108 His Collected works in two volumes collecting all the mathematical papers of Eugenio Elia Levi in a revised typographical form both amending typographical errors and author s oversights A collection of all his published papers in their original typographical form probably an unordered uncorrected collection of offprints is available online at the Internet Archive Levi Eugenio Elia Mathematical papers Los Angeles UCLA p 782 archived from the original on 9 August 2016 See also EditPseudoconvexity Levi decomposition Parametrix Several complex variablesNotes Edit This section is mainly based on the survey article by Picone 1959 included in Levi s Opere Collected works describing his researches briefly but comprehensively occasionally also the comments of Guido Fubini in Fubini amp Loria 1918 are taken into account See the two well known papers Levi 1910 and Levi 1910 Levi deals with functions of two complex variables but his calculations can be extended to functions with any finite number of variables as he explicitly states Levi following a then well established practice does not use Wirtinger derivatives References EditBiographical and general references Edit Celli Andrea Mattaliano Maurizio eds 2015 Eugenio Elia Levi le speranze perdute della Matematica italiana in Italian Milano EGEA pp LIV 326 ISBN 978 88 2384 461 2 Wide source of unpublished manuscript documents of and about E E Levi A short presentation could be found on EGEA website Coen Salvatore 1999 Beppo Levi una biografia in Levi Beppo ed Opere Volume I 1897 1926 Collected works Volume I 1897 1926 in Italian Bologna Edizioni Cremonese distributed by Unione Matematica Italiana pp XIII LIV Zbl 1054 01520 An ample biographical paper nearly 40 pages on Beppo Levi an earlier version of it was published as Coen Salvatore 1994 Beppo Levi la vita in Coen Salvatore ed Seminari di geometria Universita di Bologna Italia 1991 1993 in Italian Bologna Universita degli Studi di Bologna Dipartimento di Matematica pp 193 232 MR 1265762 Zbl 0795 01022 It gives many useful information on the family and on the relationship between the two Levi brothers D Ovidio E Bianchi L Volterra V 1912 Relazione sul premio per la Matematica relativo all anno 1912 presentata dalla Commissione composta dei Soci D Ovidio Bianchi Volterra Report on the prize for Mathematics for the year 1912 presented by the Commission consisting of Members D Ovidio Bianchi Volterra Rendiconti della Accademia Nazionale delle Scienze detta dei XL Memorie di Matematica e Applicazioni Serie 3 in Italian XVII 62 XXIV XXV archived from the original on 27 September 2011 The relation of Enrico D Ovidio Luigi Bianchi and Vito Volterra motivating their decision for the awarding of the golden medal of the Accademia Nazionale delle Scienze detta dei XL to Eugenio Elia Levi Fubini Guido Loria Gino 1918 Eugenio Elia Levi 1883 1917 Bollettino di Bibliografia e Storia delle Scienze Matematiche in Italian 20 38 45 JFM 46 0019 07 The most widely known biographical reference on Eugenio Elia Levi written by Guido Fubini and Gino Loria Loria Gino 1918 Panegirico di un Eroe Commemorazione del Prof Eugenio Elia Levi pronunziata nell aula magna dell Universita di Genova addi XXIX maggio MCMXVIII Panegyric of a Hero Commemoration of Prof Eugenio Elia Levi pronounced in the auditorium of the University of Genoa on 29 May 1918 in Italian Sestri Ponente S L A G Bruzzone e C p 31 A pamphlet containing the commemoration of Eugenio Elia Levi pronounced by Gino Loria at the University of Genova on May 29 1918 Padoa Alessandro December 1917 Eugenio Elia Levi Bollettino della Mathesis in Italian 9 89 92 Picone Mauro 1959 Sulla Vita e sulle Opere di Eugenio Elia Levi in Levi Eugenio Elia ed Opere Volume I Collected Works in Italian Roma Edizioni Cremonese distributed by Unione Matematica Italiana pp V XV MR 0123464 Zbl 0091 00108 A commemorative paper on Eugenio Elia Levi written by Mauro Picone and included in the first volume of his Opere Levi 1959 1960 Roero C S 31 January 2005 Eugenio Elia Levi 18 10 1883 28 10 1917 in Italian archived from the original on 27 September 2011 retrieved 12 January 2010 Tricomi G F 1962 Eugenio Elia Levi Matematici italiani del primo secolo dello stato unitario Italian mathematicians of the first century of the unitary state Memorie dell Accademia delle Scienze di Torino Classe di Scienze fisiche matematiche e naturali series IV in Italian vol I p 120 Zbl 0132 24405 Available from the website of the Societa Italiana di Storia delle Matematiche An ample historical paper written by Francesco Tricomi to commemorate all Italian mathematicians who worked during the first century of the Italian State Vitali Giuseppe December 1917 Eugenio Elia Levi Bollettino della Mathesis in Italian 9 86 89 External links EditComoglio Mauro 4 November 2010 La guerra del 15 18 termina il 4 Novembre Un anno prima era morto Eugenio Elia Levi in Italian MATEpristem retrieved 13 June 2011 Dell Aglio L 2005 LEVI Eugenio Elia Enciclopedia Treccani Dizionario Biografico degli Italiani in Italian vol LXIV retrieved 15 September 2011 The biographical entry about Eugenio Elia Levi in the Dizionario Biografico degli Italiani Biographical Dictionary of Italians section of the Enciclopedia Treccani Guerraggio Angelo Nastasi Pietro Tricomi Francesco 2008 2010 Eugenio Elia Levi 1883 1917 Edizione Nazionale Mathematica Italiana in Italian Scuola Normale Superiore retrieved 18 January 2011 Available from the Edizione Nazionale Mathematica Italiana Eugenio Elia Levi at the Mathematics Genealogy Project Retrieved from https en wikipedia org w index php title Eugenio Elia Levi amp oldid 1143434727, wikipedia, wiki, book, books, library,
