fbpx
Wikipedia

Gábor Szegő

May 04, 2023

Gábor Szegő (Hungarian: [ˈɡaːbor ˈsɛɡøː]) (January 20, 1895 – August 7, 1985) was a Hungarian-American mathematician. He was one of the foremost mathematical analysts of his generation and made fundamental contributions to the theory of orthogonal polynomials and Toeplitz matrices building on the work of his contemporary Otto Toeplitz.

Life

Szegő was born in Kunhegyes, Austria-Hungary (today Hungary), into a Jewish family as the son of Adolf Szegő and Hermina Neuman.[1] He married the chemist Anna Elisabeth Neményi in 1919, with whom he had two children.

In 1912 he started studies in mathematical physics at the University of Budapest, with summer visits to the University of Berlin and the University of Göttingen, where he attended lectures by Frobenius and Hilbert, amongst others. In Budapest he was taught mainly by Fejér, Beke, Kürschák and Bauer[2] and made the acquaintance of his future collaborators George Pólya and Michael Fekete. His studies were interrupted in 1915 by World War I, in which he served in the infantry, artillery and air corps. In 1918 while stationed in Vienna, he was awarded a doctorate by the University of Vienna for his work on Toeplitz determinants.[3][4] He received his Privat-Dozent from the University of Berlin in 1921, where he stayed until being appointed as successor to Knopp at the University of Königsberg in 1926. Intolerable working conditions during the Nazi regime resulted in a temporary position at the Washington University in St. Louis, Missouri in 1936, before his appointment as chairman of the mathematics department at Stanford University in 1938, where he helped build up the department until his retirement in 1966. He died in Palo Alto, California. His doctoral students include Paul Rosenbloom and Joseph Ullman. The Gábor Szegö Prize, Szegő Gábor Primary School, and Szegő Gábor Matematikaverseny (a mathematics competition in his former school) are all named in his honor.

Works

Szegő's most important work was in analysis. He was one of the foremost analysts of his generation and made fundamental contributions to the theory of Toeplitz matrices and orthogonal polynomials. He wrote over 130 papers in several languages. Each of his four books, several written in collaboration with others, has become a classic in its field. The monograph Orthogonal polynomials, published in 1939, contains much of his research and has had a profound influence in many areas of applied mathematics, including theoretical physics, stochastic processes and numerical analysis.

Tutoring von Neumann

At the age of 15, the young John von Neumann, recognised as a mathematical prodigy, was sent to study advanced calculus under Szegő. On their first meeting, Szegő was so astounded by von Neumann's mathematical talent and speed that he was brought to tears.[5] Szegő subsequently visited the von Neumann house twice a week to tutor the child prodigy. Some of von Neumann's instant solutions to the problems in calculus posed by Szegő, sketched out on his father's stationery, are now on display at the von Neumann archive at Budapest.[6]

Honours

Amongst the many honours received during his lifetime were:

Bibliography

  • The collected Papers of Gábor Szegő, 3 Vols (ed. Richard Askey), Birkhäuser, 1982, ISBN 3-7643-3063-5
  • Pólya, George; Szegő, Gábor (1972) [1925], Problems and theorems in analysis, 2 Vols, Springer-Verlag
  • Szegő, Gábor (1933), Asymptotische Entwicklungen der Jacobischen Polynome, Niemeyer[7]
  • Szegő, Gábor (1939), Orthogonal Polynomials, American Mathematical Society;[8] 2nd edn. 1955
  • Pólya, George; Szegő, Gábor (1951), Isoperimetric problems in mathematical physics, Annals of Mathematics Studies, vol. 27, Princeton University Press, ISBN 0691079889
  • Szegő, Gábor; Grenander, Ulf (1958), Toeplitz forms and their applications, Chelsea[9]

Selected articles

  • Szegő, G. (1920). "Beiträge zur Theorie der Toeplitzschen Formen". Math. Z. 6 (3–4): 167–202. doi:10.1007/bf01199955. S2CID 118147030.
  • Szegő, G. (1921). "Beiträge zur Theorie der Toeplitzschen Formen, II". Math. Z. 9 (3–4): 167–190. doi:10.1007/bf01279027. S2CID 125157848.
  • Szegő, G. (1935). "A problem concerning orthogonal polynomials". Trans. Amer. Math. Soc. 37: 196–206. doi:10.1090/s0002-9947-1935-1501782-2. MR 1501782.
    • Szego, Gabriel (1936). "Correction". Trans. Amer. Math. Soc. 39 (3): 500. doi:10.2307/1989765. JSTOR 1989765. MR 1501861.
  • Szegő, Gabriel (1936). "Inequalities for the zeros of Legendre polynomials and related functions". Trans. Amer. Math. Soc. 39: 1–17. doi:10.1090/s0002-9947-1936-1501831-2. MR 1501831.
  • Szegő, Gabriel (1936). "On some Hermitian forms associated with two given curves of the complex plane". Trans. Amer. Math. Soc. 40 (3): 450–461. doi:10.1090/s0002-9947-1936-1501884-1. MR 1501884.
  • Szegő, G. (1940). "On the gradient of solid harmonic polynomials". Trans. Amer. Math. Soc. 47: 51–65. doi:10.1090/s0002-9947-1940-0000847-6. MR 0000847.
  • with A. C. Schaeffer: Schaeffer, A. C.; Szegő, G. (1941). "Inequalities for harmonic polynomials in two and three dimensions". Trans. Amer. Math. Soc. 50 (2): 187–225. doi:10.1090/s0002-9947-1941-0005164-7. MR 0005164.
  • Szegő, G. (1942). "On the oscillations of differential transforms. I". Trans. Amer. Math. Soc. 52 (3): 450–462. doi:10.1090/s0002-9947-1942-0007170-6. MR 0007170.
  • Szegő, G. (1943). "On the oscillations of differential transforms. IV. Jacobi polynomials". Trans. Amer. Math. Soc. 53 (3): 463–468. doi:10.1090/s0002-9947-1943-0008100-4. MR 0008100.
  • with Max Schiffer: Schiffer, M.; Szegő, G. (1949). "Virtual mass and polarization". Trans. Amer. Math. Soc. 67: 130–205. doi:10.1090/s0002-9947-1949-0033922-9. MR 0033922.
  • Szegő, G. (1950). "On certain special sets of orthogonal polynomials". Proc. Amer. Math. Soc. 1 (6): 731–737. doi:10.1090/s0002-9939-1950-0042546-2. MR 0042546.
  • with Albert Edrei: Edrei, A.; Szegő, G. (1953). "A note on the reciprocal of a Fourier series". Proc. Amer. Math. Soc. 4 (2): 323–329. doi:10.1090/s0002-9939-1953-0053267-7. MR 0053267.

References

  1. ^ Biography on the homepage of Kunhegyes (in Hungarian)
  2. ^ "Biographies - Alfréd Rényi Institute of Mathematics (bios of Bauer Mihály and Beke Manó)" (PDF).
  3. ^ Gábor Szegő at the Mathematics Genealogy Project
  4. ^ Official memorial citation 2009-03-25 at the Wayback Machine, Stanford University.
  5. ^ Impagliazzo, John; Glimm, James; Singer, Isadore Manuel The Legacy of John von Neumann, American Mathematical Society, 1990, ISBN 0-8218-4219-6.
  6. ^ John Von Neumann: The Scientific Genius Who Pioneered the Modern Computer, by Norman Macrae, American Mathematical Soc., 2000, page 70
  7. ^ Shohat, J. (1935). "Szegő on Jacobi Polynomials". Bull. Amer. Math. Soc. 41 (3): 165–169. doi:10.1090/S0002-9904-1935-06050-1.
  8. ^ Shohat, J. (1940). "Review: Gabor Szegő: Orthogonal Polynomials". Bull. Amer. Math. Soc. 46 (7): 583–587. doi:10.1090/s0002-9904-1940-07231-3.
  9. ^ Spitzer, F. (1959). "Review: Ulf Grenander and Gabor Szegő, Toeplitz forms and their applications". Bull. Amer. Math. Soc. 65 (2): 97–101. doi:10.1090/s0002-9904-1959-10296-2.

External links

May 04, 2023
gábor, szegő, hungarian, ˈɡaːbor, ˈsɛɡøː, january, 1895, august, 1985, hungarian, american, mathematician, foremost, mathematical, analysts, generation, made, fundamental, contributions, theory, orthogonal, polynomials, toeplitz, matrices, building, work, cont. Gabor Szego Hungarian ˈɡaːbor ˈsɛɡoː January 20 1895 August 7 1985 was a Hungarian American mathematician He was one of the foremost mathematical analysts of his generation and made fundamental contributions to the theory of orthogonal polynomials and Toeplitz matrices building on the work of his contemporary Otto Toeplitz Gabor SzegoBust of Gabor Szego in his hometown of KunhegyesBorn 1895 01 20 20 January 1895Kunhegyes Austria Hungary now Hungary Died7 August 1985 1985 08 07 aged 90 Palo Alto California U S Alma materUniversity of ViennaKnown forFekete Szego inequalityPolya Szego inequalityGrace Walsh Szego coincidence theoremRogers Szego polynomialsSzego kernelSzego limit theoremsSzego polynomialSzego theoremSzego recurrenceScientific careerFieldsMathematicsInstitutionsUniversity of KonigsbergWashington University in St LouisStanford UniversityThesisEin Grenzwertsatz uber die Toeplitz Determinanten einer reellen Funktion 1918 Doctoral advisorWilhelm WirtingerPhilipp FurtwanglerDoctoral studentsPaul RosenbloomJoseph Ullman Contents 1 Life 2 Works 3 Tutoring von Neumann 4 Honours 5 Bibliography 6 Selected articles 7 References 8 External linksLife EditSzego was born in Kunhegyes Austria Hungary today Hungary into a Jewish family as the son of Adolf Szego and Hermina Neuman 1 He married the chemist Anna Elisabeth Nemenyi in 1919 with whom he had two children In 1912 he started studies in mathematical physics at the University of Budapest with summer visits to the University of Berlin and the University of Gottingen where he attended lectures by Frobenius and Hilbert amongst others In Budapest he was taught mainly by Fejer Beke Kurschak and Bauer 2 and made the acquaintance of his future collaborators George Polya and Michael Fekete His studies were interrupted in 1915 by World War I in which he served in the infantry artillery and air corps In 1918 while stationed in Vienna he was awarded a doctorate by the University of Vienna for his work on Toeplitz determinants 3 4 He received his Privat Dozent from the University of Berlin in 1921 where he stayed until being appointed as successor to Knopp at the University of Konigsberg in 1926 Intolerable working conditions during the Nazi regime resulted in a temporary position at the Washington University in St Louis Missouri in 1936 before his appointment as chairman of the mathematics department at Stanford University in 1938 where he helped build up the department until his retirement in 1966 He died in Palo Alto California His doctoral students include Paul Rosenbloom and Joseph Ullman The Gabor Szego Prize Szego Gabor Primary School and Szego Gabor Matematikaverseny a mathematics competition in his former school are all named in his honor Works EditSzego s most important work was in analysis He was one of the foremost analysts of his generation and made fundamental contributions to the theory of Toeplitz matrices and orthogonal polynomials He wrote over 130 papers in several languages Each of his four books several written in collaboration with others has become a classic in its field The monograph Orthogonal polynomials published in 1939 contains much of his research and has had a profound influence in many areas of applied mathematics including theoretical physics stochastic processes and numerical analysis Tutoring von Neumann EditAt the age of 15 the young John von Neumann recognised as a mathematical prodigy was sent to study advanced calculus under Szego On their first meeting Szego was so astounded by von Neumann s mathematical talent and speed that he was brought to tears 5 Szego subsequently visited the von Neumann house twice a week to tutor the child prodigy Some of von Neumann s instant solutions to the problems in calculus posed by Szego sketched out on his father s stationery are now on display at the von Neumann archive at Budapest 6 Honours EditAmongst the many honours received during his lifetime were Julius Konig Prize of the Hungarian Mathematical Society 1928 Member of the Konigsberger Gelehrten Gesellschaft 1928 Corresponding member of the Austrian Academy of Sciences in Vienna 1960 Honorary member of the Hungarian Academy of Sciences 1965 Bibliography EditThe collected Papers of Gabor Szego 3 Vols ed Richard Askey Birkhauser 1982 ISBN 3 7643 3063 5 Polya George Szego Gabor 1972 1925 Problems and theorems in analysis 2 Vols Springer Verlag Szego Gabor 1933 Asymptotische Entwicklungen der Jacobischen Polynome Niemeyer 7 Szego Gabor 1939 Orthogonal Polynomials American Mathematical Society 8 2nd edn 1955 Polya George Szego Gabor 1951 Isoperimetric problems in mathematical physics Annals of Mathematics Studies vol 27 Princeton University Press ISBN 0691079889 Szego Gabor Grenander Ulf 1958 Toeplitz forms and their applications Chelsea 9 Selected articles EditSzego G 1920 Beitrage zur Theorie der Toeplitzschen Formen Math Z 6 3 4 167 202 doi 10 1007 bf01199955 S2CID 118147030 Szego G 1921 Beitrage zur Theorie der Toeplitzschen Formen II Math Z 9 3 4 167 190 doi 10 1007 bf01279027 S2CID 125157848 Szego G 1935 A problem concerning orthogonal polynomials Trans Amer Math Soc 37 196 206 doi 10 1090 s0002 9947 1935 1501782 2 MR 1501782 Szego Gabriel 1936 Correction Trans Amer Math Soc 39 3 500 doi 10 2307 1989765 JSTOR 1989765 MR 1501861 Szego Gabriel 1936 Inequalities for the zeros of Legendre polynomials and related functions Trans Amer Math Soc 39 1 17 doi 10 1090 s0002 9947 1936 1501831 2 MR 1501831 Szego Gabriel 1936 On some Hermitian forms associated with two given curves of the complex plane Trans Amer Math Soc 40 3 450 461 doi 10 1090 s0002 9947 1936 1501884 1 MR 1501884 Szego G 1940 On the gradient of solid harmonic polynomials Trans Amer Math Soc 47 51 65 doi 10 1090 s0002 9947 1940 0000847 6 MR 0000847 with A C Schaeffer Schaeffer A C Szego G 1941 Inequalities for harmonic polynomials in two and three dimensions Trans Amer Math Soc 50 2 187 225 doi 10 1090 s0002 9947 1941 0005164 7 MR 0005164 Szego G 1942 On the oscillations of differential transforms I Trans Amer Math Soc 52 3 450 462 doi 10 1090 s0002 9947 1942 0007170 6 MR 0007170 Szego G 1943 On the oscillations of differential transforms IV Jacobi polynomials Trans Amer Math Soc 53 3 463 468 doi 10 1090 s0002 9947 1943 0008100 4 MR 0008100 with Max Schiffer Schiffer M Szego G 1949 Virtual mass and polarization Trans Amer Math Soc 67 130 205 doi 10 1090 s0002 9947 1949 0033922 9 MR 0033922 Szego G 1950 On certain special sets of orthogonal polynomials Proc Amer Math Soc 1 6 731 737 doi 10 1090 s0002 9939 1950 0042546 2 MR 0042546 with Albert Edrei Edrei A Szego G 1953 A note on the reciprocal of a Fourier series Proc Amer Math Soc 4 2 323 329 doi 10 1090 s0002 9939 1953 0053267 7 MR 0053267 References Edit Biography on the homepage of Kunhegyes in Hungarian Biographies Alfred Renyi Institute of Mathematics bios of Bauer Mihaly and Beke Mano PDF Gabor Szego at the Mathematics Genealogy Project Official memorial citation Archived 2009 03 25 at the Wayback Machine Stanford University Impagliazzo John Glimm James Singer Isadore Manuel The Legacy of John von Neumann American Mathematical Society 1990 ISBN 0 8218 4219 6 John Von Neumann The Scientific Genius Who Pioneered the Modern Computer by Norman Macrae American Mathematical Soc 2000 page 70 Shohat J 1935 Szego on Jacobi Polynomials Bull Amer Math Soc 41 3 165 169 doi 10 1090 S0002 9904 1935 06050 1 Shohat J 1940 Review Gabor Szego Orthogonal Polynomials Bull Amer Math Soc 46 7 583 587 doi 10 1090 s0002 9904 1940 07231 3 Spitzer F 1959 Review Ulf Grenander and Gabor Szego Toeplitz forms and their applications Bull Amer Math Soc 65 2 97 101 doi 10 1090 s0002 9904 1959 10296 2 External links EditO Connor John J Robertson Edmund F Gabor Szego MacTutor History of Mathematics archive University of St Andrews Askey Richard 17 May 1995 Gabor Szego One hundred years Topic 25 Op Sf Net Retrieved from https en wikipedia org w index php title Gabor Szego amp oldid 1124103852, wikipedia, wiki, book, books, library,

article

, read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.