Gaetano Fichera - Selected Publications

Selected Publications

All the works of Gaetano Fichera listed in this section, except (Fichera 1964a), (Fichera 1974a) and also its translation (Fichera 1978a), can be found in his "opere scelte" (Fichera 2004) or in the volume (Fichera 2002).

• Fichera, Gaetano (1943), "Intorno al passaggio al limite sotto il segno d'integrale", Portugaliae Mathematica (in Italian) 4 (1): 1–20, MR 0009192, Zbl 0063.01364 . In this paper (English translation of the original Italian title:–"On the passage to the limit under the sign of integral"), a necessary and sufficient condition for the exchange of the limit and the integration operations for sequences of functions is proven, in the spirit of Henri Lebesgue's Dominated convergence theorem (which, however states only a sufficient condition).
• Fichera, Gaetano (1948), "Teoremi di completezza sulla frontiera di un dominio per taluni sistemi di funzioni", Annali di Matematica Pura e Applicata, Serie IV (in Italian) 27 (1–2): 1–28, doi:10.1007/BF02415556, MR 0029014, Zbl 0035.34801 . "Completeness theorems on the boundary of a domain for certain systems of functions" is a classical paper in potential theory.
• Fichera, Gaetano (1949), "Analisi esistenziale per le soluzioni dei problemi al contorno misti, relativi all'equazione e ai sistemi di equazioni del secondo ordine di tipo ellittico, autoaggiunti", Annali della Scuola Normale Superiore, Serie III (in Italian), 1 (1947)) (1–4): 75–100, MR 0035370, Zbl 0035.18603 . The paper "Existential analysis of the solutions of mixed boundary value problems, related to second order elliptic equation and systems of equations, selfadjoint" contains the first proofs of existence and uniqueness theorems for the mixed boundary value problem for fairly general domains.
• Fichera, Gaetano (1954), "Sulla derivazione delle funzioni additive d'insieme", Rendiconti del Seminario Matematico della Università di Padova (in Italian) 23: 366–397, MR 0064858, Zbl 0058.28302 . The paper "On the differentiation of additive set functions" is an important contribution to measure theory where the Radon–Nikodym theorem is extended in order to include singular finitely additive measures.
• Fichera, Gaetano (1955a), "Alcuni recenti sviluppi della teoria dei problemi al contorno per le equazioni alle derivate parziali lineari", in Fichera, G., Convegno Internazionale sulle Equazioni Lineari alle Derivate Parziali – Trieste 25–28 Agosto 1954 (in Italian), Roma: Edizioni Cremonese, pp. 174–227, MR 0074665, Zbl 0068.31101 . The paper Some recent developments of the theory of boundary value problems for linear partial differential equations details Fichera's approach to a general theory of boundary value problems for linear partial differential equations through a theorem similar in spirit to the Lax–Milgram theorem: as an application, the general existence and uniqueness theorems of previous paper (Fichera 1949) are proved dropping the hypothesis of self-adjointness of the linear partial differential operators considered.
• Fichera, Gaetano (1955b), "Su un metodo del Picone per il calcolo degli autovalori e delle autosoluzioni", Annali di Matematica Pura e Applicata, 4 (in Italian) 40 (1): 239–259, doi:10.1007/BF02416536, MR 0075569, Zbl 0065.35501 . English translation of the title:-"On a method of Picone for the calculus of eigenvalues and eigensolutions".
• Fichera, Gaetano (1956), "Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine", Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali, Serie VIII (in Italian) 5 (1): 1–30, MR 0089348, Zbl 0075.28102 . On linear elliptic-parabolic equations of second order(English translation of the title) is the first paper on the theory of partial differential equations of non positive characteristics: the Fichera's function is introduced and its applications to the boundary value problems for this class of operators is detailed. Also the well posedness is considered.
• Fichera, Gaetano (1957), "Caratterizzazione della traccia, sulla frontiera di un campo, di una funzione analitica di più variabili complesse", Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali, VIII (in Italian) 22 (6): 706–715, MR 0093597, Zbl 0106.05202 . "Characterization of the trace, on the boundary of a domain, of an analytic function of several complex variables" (English translation of the title) is an epoch-making paper in the theory of CR-functions, where the Dirichlet problem for analytic functions of several complex variables is solved for general data.
• Fichera, Gaetano (1961a), "Spazi lineari di k–misure e di forme differenziali", Proceedings of the Symposium on Linear Spaces, Jerusalem, 1960 (in Italian), Jerusalem / Oxford: Jerusalem Academic Press / Pergamon Press, pp. 175–226, MR 0133434, Zbl 0126.17801 . English translation of the title:-"Linear spaces of k–measures and differential forms". Perhaps the most important contribution of Gaetano Fichera to the theory of exterior differential forms: k–measures are introduced and, despite being less general than currents and thus being easier to work with, it is proved that all the most important results of the theory can be obtained using them.
• Fichera, Gaetano (1960), "On a unified theory of boundary value problems for elliptic-parabolic equations of second order", in Langer, Rudolph E., Boundary Problems in Differential Equations, Madison: The University of Wisconsin Press, pp. 97–120, MR 0111931, Zbl 0122.33504 . A paper about the boundary value problem for partial differential equations of non positive characteristics, where the Fichera's function is introduced and its application are described.
• Fichera, Gaetano (1961b), "Teoria assiomatica delle forme armoniche", Rendiconti di Matematica e delle sue applicazioni, 5 (in Italian) 20: 147–171, MR 0140124, Zbl 0116.07601 . A paper containing an abstract theory harmonic forms in Hilbert spaces, including a proof of Hodge theorem: an English translation of the title is:-"Axiomatic theory of harmonic forms".
• Fichera, Gaetano (1961c), "Il teorema del massimo modulo per l'equazione dell'elastostatica tridimensionale", Archive for Rational Mechanics and Analysis (in Italian) 7 (5): 373–387, Bibcode:1961ArRMA...7..373F, doi:10.1007/BF00250770, Zbl 0100.30801 . "The maximum modulus theorem for the three-dimensional elastostatic equation" is the article where the now called "Fichera maximum principle" is proved.
• Fichera, Gaetano (1963), "Sul problema elastostatico di Signorini con ambigue condizioni al contorno (On the elastostatic problem of Signorini with ambiguous boundary conditions)", Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali, Serie VIII, (in Italian) 34 (2): 138–142, Zbl 0128.18305 . A short paper describing briefly the approach to the solution of the Signorini problem.
• Fichera, Gaetano (1964a), "Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno (Elastostatic problems with unilateral constraints: the Signorini problem with ambiguous boundary conditions)", Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali, Serie VIII, (in Italian) 7 (2): 91–140, Zbl 0146.21204 . The paper containing the existence and uniqueness theorem for the Signorini problem, translated in the English language as Fichera, Gaetano (1964b), "Elastostatic problems with unilateral constraints: the Signorini problem with ambiguous boundary conditions", Seminari dell'istituto Nazionale di Alta Matematica 1962–1963, Rome: Edizioni Cremonese, pp. 613–679 .
• Fichera, Gaetano (1964c), "Semicontinuity of multiple integrals in ordinary form", Archive for Rational Mechanics and Analysis 17 (5): 339–352, Bibcode:1964ArRMA..17..339F, doi:10.1007/BF00250470, Zbl 0128.10003 . A paper where a semicontinuity theorem is proved for a functional depending on general linear operators (not simply partial differential operators).
• Fichera, Gaetano (1972a), "Existence theorems in elasticity", in Flügge, Siegfried; Truesdell, Clifford A., Festkörpermechanik/Mechanics of Solids, Handbuch der Physik (Encyclopedia of Physics), VIa/2, Berlin–Heidelberg–New York: Springer-Verlag, pp. 347–389, Zbl 0277.73001 .
• Fichera, Gaetano (1972b), "Boundary value problems of elasticity with unilateral constraints", in Flügge, Siegfried; Truesdell, Clifford A., Festkörpermechanik/Mechanics of Solids, Handbuch der Physik (Encyclopedia of Physics), VIa/2 (paperback 1984 ed.), Berlin–Heidelberg–New York: Springer-Verlag, pp. 391–424, ISBN 3-540-13161-2, ISBN 0-387-13161-2 Check |isbn= value (help), Zbl 0277.73001 . The encyclopedic entry about problems with unilateral constraints (the class of boundary value problems the Signorini problem belongs to) he wrote for the Handbuch der Physik on invitation by Clifford Truesdell.
• Fichera, Gaetano (1974a), "Metodi e risultati concernenti l'analisi numerica e quantitativa (Methods and results concerning numerical and quantitative analysis)", Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali, Serie VIII, (in Italian) 12 (1): 1–202, Zbl 0334.65002 . An extensive survey on some problems of numerical analysis (and associate problems of mathematical analysis) studied by Gaetano Fichera and his group of students: its updated English translation is (Fichera 1978a).
• Fichera, Gaetano (1974b), "On the approximation of analytic functions by rational functions", Journal of Mathematical and Physical Science (Madras) 8 (1): 7–19, Zbl 0294.30034 . A survey paper about the theory of approximation of and by analytic functions of a complex variable.
• Fichera, Gaetano (1975), "Comportamento asintotico del campo elettrico e della densità elettrica in prossimità dei punti singolari della superficie conduttore", Rendiconti del Seminario Matematico dell'Università e Politecnico di Torino (in Italian), 32 (1973–74): 111–143, Zbl 0318.35007 . Asymptotic behavior of the electric field and density of the electric charge in the neighborhood of singular points of a conducting surface (English translation of the title) is an important paper on the asymptotic analysis of the electric field near the vertex of a conical conducting surface. There exists also a freely consultable Russian translation, "Асимптотическое поведение электрического поля и плотности электрического заряда в окрестности сингулярных точек проводящей поверхности", Uspekhi Matematicheskikh Nauk (in Russian) 30 (3(183)), 1975: 105–124, MR 388978, Zbl 0318.35007 .
• Fichera, Gaetano (1976), "Asymptotic behaviour of the electric field near the singular points of the conductor surface", Rendiconti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, 8 60 (1): 13–20, Zbl 0364.35004 .
• Fichera, Gaetano; Sneider, Maria A.; Wyman, Jeffreys (1977), "On the existence of a steady state in a biological system", Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali, Serie VII, Sezione III XIV (1): 1–26, Zbl 0414.92004 . A research announcement related to the survey paper (Fichera 1978b).
• Fichera, Gaetano; Sneider, Maria Adelaide; Wyman, Jeffreys (1977a), "On the existence of a steady state in a biological system", PNAS 74 (10): 4182–4184, Bibcode:1977PNAS...74.4182F, doi:10.1073/pnas.74.10.4182 . A research announcement related to the survey paper (Fichera 1978b).
• Fichera, Gaetano (1978a), Numerical and quantitative analysis. Translated from Italian by Sandro Graffi, Surveys and Reference Works in Mathematics 3, London–San Francisco–Melbourne: Pitman Publishing, pp. x+208, ISBN 0-273-00284-8, MR 0519677, Zbl 0384.65043 . An English updated translation of the memoir (Fichera 1974a).
• Fichera, Gaetano (1978b), "Un problema di analisi matematica proposto dalla biologia", Rendiconti di Matematica e delle sue applicazioni, 6 (in Italian) 10 (4): 1–6, MR 0503945, Zbl 0378.34039 . A survey paper on an interdisciplinary research conducted by him, Maria Adelaide Sneider and Jeffries Wyman, on the existence of a steady state in a biological system. An English translation of the title is:-"A problem in mathematical analysis proposed by biology".
• Fichera, Gaetano (Gennaio–Aprile 1979), "Il contributo italiano alla teoria matematica dell'elasticità", Rendiconti del Circolo Matematico di Palermo, Serie II, (in Italian), Tomo XXVIII (1): 5–26, doi:10.1007/BF02849579, MR 0564544, Zbl 0433.73002 . The text of the address of Gaetano Fichera given on the occasion of the conferment of the laurea honoris causa in civil engineering: he describes the history of the theory of elasticity detailing particularly the contributions of Italian scientists.
• Fichera, Gaetano (1979a), "Remarks on Saint-Venant's principle", Rendiconti di Matematica e delle sue applicazioni, 6 12: 181–200, Zbl 0443.73002 . A paper containing a mathematical proof of the Saint-Venant's principle.
• Fichera, Gaetano (1979b), "Avere una memoria tenace crea gravi problem (Having a tenacious memory creates serious problems)", Archive for Rational Mechanics and Analysis (in Italian) 70 (2): 373–387, doi:10.1007/BF00281161, Zbl 0425.73002 .
• Fichera, Gaetano (1979c), "The problem of the completeness of systems of particular solutions of partial differential equations", in Ansorge, R.; Glashoff, K.; Werner, B., Numerical mathematics, Symposium on the Occasion of Retirement of Lothar Collatz, Hamburg 1979, International Series of Numerical Mathematics 49, Basel: Birkhäuser-Verlag, pp. 25–41, Zbl 0434.35010 .
• Fichera, Gaetano (1982a), "Problemi al contorno per le funzioni pluriarmoniche", Atti del Convegno celebrativo dell'80° anniversario della nascita di Renato Calapso, Messina–Taormina, 1–4 aprile 1981 (in Italian), Roma: Libreria Eredi Virgilio Veschi, pp. 127–152, MR 0698973, Zbl 0958.32504 . A paper where a trace condition for pluriharmonic functions is given. An English translation of the title is:-"Boundary value problems for pluriharmonic functions".
• Fichera, Gaetano (1982b), "Valori al contorno delle funzioni pluriarmoniche: estensione allo spazio di un teorema di L. Amoroso", Rendiconti del Seminario Matematico e Fisico di Milano (in Italian) 52 (1): 23–34, doi:10.1007/BF02924996, MR 0802991, Zbl 0569.31006 . An English translation of the title is:-"Boundary values of pluriharmonic functions: extension to the space of a theorem of L. Amoroso".
• Fichera, Gaetano (1982c), "Su un teorema di L. Amoroso nella teoria delle funzioni analitiche di due variabili complesse", Revue Roumaine de Mathématiques Pures et Appliquées (in Italian) 27: 327–333, MR 0669481, Zbl 0509.31007 . In this paper, it is proved that a necessary and sufficient condition for an harmonic function defined on a ball in ℂ2 to be pluriharmonic is to satisfy the Amoroso integral equation: an English translation of the title is:-"On a theorem of L. Amoroso in the theory of analytic functions of two complex variables.
• Fichera, Gaetano (1983), "Sul teorema di Cauchy–Morera per le funzioni analitiche di più variabili complesse", Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali, Series VIII (in Italian) 74 (6): 336–350, Zbl 0573.32005 . In the article "On the theorem of Cauchy–Morera for analytic functions of several complex variables, Morera's theorem for analytic functions of several complex variables is proved under the sole hypothesis of local integrability for the given function .
• Fichera, Gaetano (1986), "Unification of global and local existence theorems for holomorphic functions of several complex variables", Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali, Serie VIII 18 (3): 61–83, MR 0917525, Zbl 0705.32006 . A paper describing the ideas of (Fichera 1957), giving some extensions of those ideas and a solution for a particular Cauchy problem for holomorphic functions of several variables.
• Fichera, Gaetano (1991), "Ricordo di Renato Caccioppoli", Ricerche di Matematica (in Italian) 40 (supplement): 11–15, Zbl 0788.01051 . Some recollections of his close friend Renato Caccioppoli.
• Fichera, Gaetano (1993), "Il calcolo infinitesimale alle soglie del Duemila", Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Supplemento, Serie IX, 4 (1): 69–86 . "Infinitesimal calculus at the threshold of the Millennium" is a survey paper by Gaetano Fichera, describing the development of infinitesimal calculus during the twentieth century and trying to trace possible scenarios for its future evolution.
• Fichera, Gaetano (1995a), "L'ultima lezione", Rendiconti della Accademia Nazionale delle Scienze detta dei XL, Memorie di Matematica e Applicazioni (in Italian) 19 (1): 1–24, MR 1387547 . His "last lesson" of the course of higher analysis, give on the occasion of his retirement from university teaching in 1992.
• Fichera, Gaetano (1995b), "La nascita della teoria delle disequazioni variazionali ricordata dopo trent'anni", Incontro scientifico italo-spagnolo. Roma, 21 ottobre 1993, Atti dei Convegni Lincei (in Italian) 114, Roma: Accademia Nazionale dei Lincei, pp. 47–53 . The birth of the theory of variational inequalities remembered thirty years later (English translation of the title) tell the story of the beginning of the theory of variational inequalities from the point of view of its founder.
• Fichera, Gaetano (1996), "Rivisitazione e storia due aspetti contrastanti della storiografia scientifica", in Tarozzi, Gino, Convegno "Giuseppe Geminiani", Cesena 16–19 October 1995 (in Italian), Cesena–Urbino . "Revisiting and history: two conflicting aspects of scientific historiography" details its author's opinions about the way of doing historical researches on mathematical topics.
• Fichera, Gaetano (1997), "A boundary value problem connected with response of semi-space to a short laser pulse", Atti della Accademia Nazionale dei Lincei, Rendiconti Lincei, Matematica e Applicazioni, Serie IX, 8 (4): 197–228, MR 1611621, Zbl 0903.35034 . Gaetano Fichera last, postumhous scientific paper, prepared for the publication by Olga Arsenievna Oleinik and his wife.
• Fichera, Gaetano (2002), Opere storiche biografiche, divulgative (in English and Italian), Napoli: Giannini / Società Nazionale di Scienze, Lettere e Arti in Napoli, p. 491 . Gaetano Fichera's "Historical, biographical, expository works": a volume collecting his contributions to the fields of history of mathematics and scientific expository work.
• Fichera, Gaetano (2004), Opere scelte (in Italian), Firenze: Edizioni Cremonese (distributed by Unione Matematica Italiana), pp. XXIX+432 (vol. 1), pp. VI+570 (vol. 2), pp. VI+583 (vol. 3) ISBN 88-7083-811-0 (vol. 1), ISBN 88-7083-812-9 (vol. 2), ISBN 88-7083-813-7 (vol. 3). His "Selected works": three volumes collecting the most important mathematical papers of Gaetano Fichera, with a biographical sketch of Olga A. Oleinik