Georges Giraud

Georges Julien Giraud^[3] (22 July 1889^[1] – 16 March 1943) was a French mathematician, working in potential theory, partial differential equations, singular integrals and singular integral equations:^[4] he is mainly known for his solution of the regular oblique derivative problem and also for his extension to n–dimensional (n ≥ 2) singular integral equations of the concept of symbol of a singular integral, previously introduced by Solomon Mikhlin.^[5]

Georges Giraud
Born	(1889-07-22)22 July 1889^[1] Saint-Étienne^[2]
Died	16 March 1943(1943-03-16) (aged 53) Bonny-sur-Loire
Nationality	French
Alma mater	École Normale Supérieure 1915
Known for	potential theory partial differential equations singular integrals singular integral equations
Awards	Prix Francœur (1919) Prix Gustave Roux (1923) Hirn Foundation prize (1925 and 1935) Grand Prix for mathematical sciences (1928) Prix Houllevigue (1930) Lasserre foundation prize (1930) Prix Saintour (1933) Prize of the Annali della Reale Scuola Normale Superiore di Pisa (1935)
Scientific career
Institutions	Université Clermont-Ferrand (now Université Blaise Pascal).
Doctoral advisor	Charles Émile Picard

Biography

Honors

Georges Giraud a été plusieurs fois lauréat de notre Académie.^[6]

— Élie Cartan, (Cartan 1943, p. 518).

The scientific work of Georges Giraud was widely acknowledged and earned him several prizes, mainly, but not exclusively, awarded him by the French Academy of Sciences: he was seven times recipient of academy prizes.

In 1919, he was awarded the "Prix Francœur" for his work on the theory of automorphic functions:^[7] the members of the commission who examined his work and nominated him were Camille Jordan, Paul Appell, Marie Georges Humbert, Jacques Hadamard, Édouard Goursat, Joseph Boussinesq, Léon Lecornu and Emile Picard (the relator).^[8] For the same motivation,^[9] On 17 December 1923 he was awarded the "Gustave Roux" prize.^[10]

In 1924 he won the Hirn Foundation Prize, for his whole scientific work:^[11] he won again the same prize in 1935,^[12] for his work on singularities of boundary value problems in the theory of partial differential equations.^[13]

In 1928 Giraud won the "Grand Prix des sciences Mathématiques" for his work in the theory of partial differential equations:^[14] for the same motivation, in 1930 he was also awarded the "Prix Houllevigue".^[15] In the same year, he was also awarded the prize of the Lasserre foundation.^[16]

In 1933 he was recipient of the Prix Saintour, for his work on partial differential and integral equations.^[17]

Finally, in 1935, apart from winning the Hirn foundation prize for a second time,^[12] he was awarded the prize of the Annali della Reale Scuola Normale Superiore di Pisa, equally divided between him, Guido Ascoli and Pietro Buzano:^[18] the members of the jury who awarded ex-aequo the prize were Guido Fubini, Mauro Picone and Giovanni Sansone.^[19]

On 14 December 1936, following up a proposal Jacques Hadamard made since 1931,^[20] he was elected corresponding member of the French Academy of Sciences.^[21]

He was also a member of the Société Mathématique de France from 1913 to his death.^[22]

Selected publications

Articles

• Giraud, Georges (1915), "Sur une classe de groupes discontinus de transformations birationnelles quadratiques et sur les fonctions de trois variables indépendantes restant invariables par ces transformations" [On a class of discontinuous groups of birational quadratic transformations and the functions of three independent variables which are invariant respect to these transformations], Annales Scientifiques de l'École Normale Supérieure, Série 3 (in French), 32: 237–403, JFM 45.1410.03.
• Giraud, Georges (1934), "Équations à intégrales principales; étude suivie d'une application" [Principal integral equations; a study followed by an application], Annales Scientifiques de l'École Normale Supérieure, 3 (in French), 51: 251–372, MR 1509344, Zbl 0011.21604, available at NUMDAM. This is one of the first papers, together with independent works of Francesco Tricomi and Solomon Mikhlin, dealing with the multidimensional theory of singular integrals.
• Giraud, Georges (29 June 1936), "Sur une classe générale d'équations à intégrales principales" [On a general class of principal integral equations], Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 202: 2124–2127, JFM 62.0498.01, Zbl 0014.30903, available at Gallica. In this short note, Giraud extends (without proof) the formula for the composition of two 2-dimensional singular integral operators using their symbols, introduced shortly before by Solomon Grigor'evich Mikhlin, to higher dimensional singular integrals.

Books

• Giraud, Georges (22 January 1916), Sur une classe de groupes discontinus de transformations birationnelles quadratiques et sur les fonctions de trois variables indépendantes restant invariables par ces transformations [On a class of discontinuous groups of birational quadratic transformations and the functions of three independent variables which are invariant respect to these transformations], Thèse (in French), Paris: Gauthier-Villars, pp. viii+167, JFM 46.0621.02. Georges Giraud's doctoral thesis, published also as (Giraud 1915).
• Giraud, Georges (1920), Leçons sur les fonctions automorphes. Fonctions automorphes de n variables, fonctions de Poincaré [Lectures on automorphic functions. Automorphic functions of n variables, Poincaré's functions], Collection de monographies sur la théorie des fonctions (in French), Paris: Gauthier-Villars, p. 123, JFM 47.0366.01, available from the Internet Archive.
• Bouligand, G.; Giraud, G.; Delens, P. (1935), Le problème de la dérivée oblique en théorie du potentiel [The oblique derivative problem in potential theory], Actualités Scientifiques et Industrielles (in French), vol. No. 219 (6), Paris: Hermann, p. 78, JFM 61.1263.01, Zbl 0012.16605, reviewed also by Murnaghan, F. D. (1936), "Review: G. Bouligand, G. Giraud and P. Delens, Le Problème de la Dérivée Oblique en Theorie du Potentiel", Bulletin of the American Mathematical Society, 42 (11): 794, doi:10.1090/S0002-9904-1936-06438-4.
• Ascoli, G.; Burgatti, P.; Giraud, G. (1936), Equazioni alle derivate parziali dei tipi ellittico e parabolico [Partial differential equations of elliptic and parabolic type] (in Italian), Firenze: Sansoni Editore, pp. IV + 186, JFM 62.0547.04 (available from the "Edizione Nazionale Mathematica Italiana"). A book collecting the winning papers of the 1935 prize of the Annali della Reale Scuola Normale Superiore di Pisa.

See also

• Cauchy principal value
• Potential theory
• Singular integral

Notes

1. According to the brief commemoration by Bertrand (1943b, p. 629): the "Georges Giraud" entry in the Enciclopedia Treccani states that he was born on 11 July 1889, and Tampieri (2014, p. 88) uses this source.
2. According to Bertrand (1943b, p. 629) and to the "Georges Giraud" entry in the Enciclopedia Treccani.
3. According to the year 1939 list of corresponding members of the "Geometry" section of the French Academy, this was his full name: however, he simply sign himself as "Georges Giraud" in all his scientific works.
4. See (Tricomi 1967, p. 21) and (Tampieri 2014, p. 89 and p. 90).
5. He announced his results in the short communication (Giraud 1936), without proof and acknowledging the previous work of Mikhlin. As a matter of fact, it was Mikhlin who gave the first proofs of these formulas, completing his work on the 2-dimensional theory: see (Mikhlin 1965, p. 9) or the entry "Singular integrals" for a comprehensive historical survey.
6. (English translation): "Georges Giraud was several times recipient of our Academy".
7. See the 22 December 1919 relation on the Prix Francœur in the "Comptes rendus".
8. Ibid. (1919, p. 1202).
9. See the 17 December 1923 relation on the Prix Gustave Roux in the "Comptes rendus", and reference (AMS 1924, p. 282).
10. According to the 17 December 1923 relation on the Prix Gustave Roux in the "Comptes rendus", the members of the examining commission were Albin Haller, Guillaume Bigourdan, Antoine Lacroix, Léon Guignard, Paul Appell, and Emile Picard again as the relator.
11. See the 22 December 1924 relation on the Hirn Foundation prize in the "Comptes rendus", and reference (AMS 1925, p. 282). According to the first reference, the amount of the prize was 2500 French francs.
12. See the 16 December 1935 relation on the Hirn Foundation prize in the "Comptes rendus", and reference (AMS 1936, p. 172).
13. "..., pour sex travaux sul les singularités dans les problèmes aux limites de la théorie des équations aux dérivées partielles", as it is precisely stated in the relation on the 1935 Hirn Foundation prize.
14. See the 17 December 1928 relation on the Gran Prix des sciences mathématiques in the "Comptes rendus", and reference (AMS 1929, p. 281).
15. See the 15 December 1930 relation on the Prix Houllevigue in the "Comptes rendus", and reference (AMS 1931, p. 281).
16. See (AMS 1931, p. 281).
17. See the 11 December 1933 relation on the Prix Saintour in the "Comptes rendus", and reference (AMS 1934, p. 205).
18. See (AMS 1936, p. 178) and (Tonelli 1936, p. III).
19. According to (Tonelli 1936), who reports excerpts from the conclusive relation of the jury. (Tonelli 1936, p. IV) states also that the amount of the prize awarded to each of the three winners was 2000 Italian Liras.
20. See (Tampieri 2014, p. 89). Precisely, Jacques Hadamard presented Giraud for the election as corresponding member of the French Academy for three times, the first two being on 12 and on 26 January 1931.
21. See the obituary notices by Cartan (1943, p. 518), Bertrand (1943b, p. 629) and Tampieri (2014, p. 89), and also the 14 December 1936 announcement of his election reporting the detailed election results.
22. See reference (SMF 1946, p. 2).

References

Biographical references

• AMS (1924), "Notes", Bulletin of the American Mathematical Society, 30 (5–6): 280–284, doi:10.1090/S0002-9904-1924-03925-1.
• AMS (1925), "Notes", Bulletin of the American Mathematical Society, 31 (5–6): 280–284, doi:10.1090/S0002-9904-1925-04060-4.
• AMS (1929), "Notes", Bulletin of the American Mathematical Society, 35 (2): 279–283, doi:10.1090/S0002-9904-1929-04731-1.
• AMS (1931), "Notes", Bulletin of the American Mathematical Society, 37 (3): 157–163, doi:10.1090/S0002-9904-1931-05122-3.
• AMS (1934), "Notes", Bulletin of the American Mathematical Society, 40 (3): 204–208, doi:10.1090/S0002-9904-1934-05817-8.
• AMS (1935), "Notes", Bulletin of the American Mathematical Society, 41 (3): 177–181, doi:10.1090/S0002-9904-1935-06071-9.
• AMS (1936), "Notes", Bulletin of the American Mathematical Society, 42 (3): 172–175, doi:10.1090/S0002-9904-1936-06270-1.
• Bertrand, Gabriel (29 March 1943a), "Decés de M. Georges Giraud" [Death of Mr. Georges Giraud], Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 216: 429, available at Gallica. The announcement of the death of Georges Giraud given at the seance of 29 March 1943 at the French Academy.
• Bertrand, Gabriel (20 December 1943b), "Allocution", Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 217: 625–640, available at Gallica. The "Address" of Gabriel Bertrand of 20 December 1943 at the French Academy: he gives biographical sketches of the lives of recently deceased members, including Pieter Zeeman, David Hilbert and Georges Giraud.
• Istituto dell'Enciclopedia Italiana (2008), "Giraud, Georges", Enciclopedia Treccani (in Italian), retrieved 16 November 2012. The biographical entry about Georges Giraud at the Enciclopedia Treccani.
• Les Secrétaires Perpétuelles (22 December 1919), "Prix Francœur", Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 169: 1202 (Giraud and other prize recipients thanks are reported at p. 322 of the same volume), available at Gallica.
• Les Secrétaires Perpétuelles (17 December 1923), "Prix Gustave Roux", Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 177: 1412, available at Gallica.
• Les Secrétaires Perpétuelles (22 December 1924), "Fondation Hirn", Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 179: 1547 (Giraud and other prize recipients thanks are reported at p. 1580 of the same volume), available at Gallica.
• Les Secrétaires Perpétuelles (17 December 1928), "Prix fonde par l'État. Grand Prix des sciences mathématiqes" [State prize. Grand prize of mathematical sciences], Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 187: 1239 (Giraud and other prize recipients thanks are reported at p. 1270 of the same volume), available at Gallica.
• Les Secrétaires Perpétuelles (15 December 1930), "Prix Houllevigue", Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 191: 1233 (Giraud and other prize recipients thanks are reported at p. 1270 of the same volume), available at Gallica.
• Les Secrétaires Perpétuelles (11 December 1933), "Prix Saintour", Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 197: 1529 (Giraud and other prize recipients thanks are reported at p. 1562 of the same volume), available at Gallica.
• Les Secrétaires Perpétuelles (16 December 1935), "Fondation Hirn", Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 201: 1289 (Giraud and other recipients thanks are reported at p. 1308 of the same volume), available at Gallica.
• Les Secrétaires Perpétuelles (14 December 1936), "Élections", Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 203: 1308, available at Gallica. The announcement of the election of Georges Giraud as corresponding member of the "Geometry" section of the French Academy.
• Les Secrétaires Perpétuelles (1 January 1939), "État de l'Académie des Sciences. Correspondants. Sciences Mathématiques. Section Ire. – Géométrie" [Status of the Academy of Sciences. Corresponding members. Mathematical sciences. First Section – Geometry], Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 208: 9, available at Gallica. The year 1939 list of corresponding members of the "Geometry" section of the French Academy.
• SMF (1946), "Vie de la société" [Life of the society], Bulletin de la Société Mathématique de France (in French), 74: 1–3, available at NUMDAM.
• Tonelli, Leonida (1936), "Prefazione" (PDF), in Ascoli, G.; Burgatti, P.; Giraud, G. (eds.), Equazioni alle derivate parziali dei tipi ellittico e parabolico [Partial differential equations of elliptic and parabolic type] (in Italian), Firenze: Sansoni Editore, pp. III–IV, JFM 62.0547.04 (available from the "Edizione Nazionale Mathematica Italiana"). The "Preface" of Leonida Tonelli to the book (Ascoli, Burgatti & Giraud 1936).

General references

• Cartan, Élie (14 April 1943), "Notice necrologique sur Georges Giraud" [Obituary of Georges Giraud], Comptes rendus hebdomadaires des séances de l'Académie des sciences (in French), Paris, 216: 516–518, MR 0010144, Zbl 0028.19503, available at Gallica.
• Tampieri, Daniele (February 2014), "Giraud, Georges", L'Archicube (in French), 15 bis (Numéro spécial): 88–92. A short "notice nécrologique" (obituary) published on the periodic special issue dedicated to obituary notices of the journal of the A–Ulm, the association of former students, students and friends of the École Normale Supérieure.

References describing the scientific contributions of Giraud

• Mikhlin, Solomon G. (1965), Multidimensional singular integrals and integral equations, International Series of Monographs in Pure and Applied Mathematics, vol. 83, Oxford-London-Edinburgh-New York-Paris-Frankfurt: Pergamon Press, pp. XII+255, MR 0185399, Zbl 0129.07701. A masterpiece in the multidimensional theory of singular integrals and singular integral equations summarizing all the results from the beginning to the year of publication, and also sketching the history of the subject.
• 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.
• Prössdorf, S. (1991), "Linear Integral Equations", in Maz'ya, V. G.; Nikol'skiǐ, S. M. (eds.), Analysis IV, Encyclopaedia of Mathematical Sciences, vol. 27, Berlin–Heidelberg–New York: Springer-Verlag, pp. 1–125, ISBN 0-387-51997-1, MR 1098506, Zbl 0780.45001 (also available as ISBN 3-540-51997-1).
• Tricomi, Francesco G. (1967), La mia vita di matematico attraverso la cronistoria dei miei lavori. (Bibliografia commentata 1916–1967) [My life as a mathematician seen through the chronicle of my works. (Annotated bibliography 1916–1967)] (in Italian), Padova: CEDAM – Casa Editrice Dott. Antonio Milani, pp. XII+172, ISBN 978-88-13-32679-1, MR 0274255, Zbl 0199.28603, is an annotated bibliography written by Francesco Tricomi in order to give a complete survey of his scientific work.