Gustav Herglotz

Gustav Herglotz Ferdinand Maria ( born February 2, 1881 in Wallern, Bohemian Forest, † March 22, 1953 in Göttingen ) was a German mathematician.

Life

Herglotz studied from 1899 at the University of Vienna mathematics and astronomy, where he spent his youth, and heard, inter alia lectures by Ludwig Boltzmann. During his studies he completed a close friendship with his fellow student Paul Ehrenfest, Hans Hahn and Heinrich Tietze. In 1900 he went to Munich and received his PhD in 1902 at Hugo von Seeliger in Astronomy ( with a work that should theoretically explain the strong variations in brightness of the newly discovered asteroid Eros, which was followed by Herglotz from its elongated shape). After that he went to Göttingen in 1902, where he habilitated in 1904 at Felix Klein. In 1904 he became a lecturer in astronomy and mathematics and in 1907 associate professor. In his time in Göttingen, he began also for the theory of earthquakes to be interested, and in collaboration with Emil Wiechert, who was then Göttingen expanded into a center of earthquake research, he developed the Wiechert- Herglotz method to determine the velocity distribution in the Earth's interior from the known terms of seismic waves (ie an inverse problem ). Herglotz solved doing a special integral equation ( the Abel - type ). In 1908 he became an associate professor in Vienna, but went in 1909 as a full professor in Leipzig. 1925 until his retirement in 1947 he was back in Göttingen, succeeding Carl Runge in the chair of applied mathematics.

Herglotz made ​​contributions in many areas of applied and pure mathematics. The set of Herglotz from differential geometry is known: On each Eifläche ( closed convex surface) of the three-dimensional real space, there are at least three closed geodesics. In applied mathematics he studied in addition to celestial mechanics, inter alia, with the beginning of the 20th century, current issues electron theory of special relativity (1910 ), where he developed a relativistic elasticity theory of general relativity, as well as hydrodynamics and diffraction theory. In analysis he made, inter alia, contributions to the theory of differential equations and potential theory. Even number theory he made ​​contributions ( theory of Dirichlet series 1905).

Among his pupils was Emil Artin, who earned his doctorate at him in Leipzig in 1921.

Works (selection and online reach work )

  • Collected Writings / Gustav Herglotz. Ed in Auftr d Acad of Sciences. in Göttingen by Hans Schwerdtfeger. XL, 652 pp., Vandenhoeck and Ruprecht, Göttingen 1979, ISBN 3-525-40720-3.
  • Lectures on the mechanics of continua / G. Herglotz. Ausarb. RB Guenther and H. Schwerdtfeger, Teubner Archive for mathematics; Vol 3, p 251: 1 Ill., graph. Darst; 22 cm, Teubner, Leipzig 1985.
  • With Isay Schur, Georg Pick, Rolf Nevanlinna, Hermann Weyl: Selected papers on the origins of the Schur Analysis. Edited and with an afterword by B. Fritzsche and B. Kirstein. Teubner Archive for mathematics; Vol 16, 290 S.: Ill., graph. Darst; Photo Mechanical Nachdr, Teubner Stuttgart Leipzig 1991, ISBN 3-8154-2012-1. This Herglotz: About power series with positive real is part of the unit circle, Ber. royal on d Ratio d. sächs Gesellsch. d Scientific. 1911
  • About the analytic continuation of the potential inside the attracting masses, Price writings of the Princely Jablonowskischen society Leipzig, VII, 52 pages, 18 Figures; Teubner, Leipzig ( 1914).
  • To Einstein 's theory of gravitation, Ber. royal on d Ratio d. sächs Gesellsch. d Scientific. Leipzig, pp. 199-203 (1916).
  • About the quadratic reciprocity law in imaginary quadratic fields, Ber. royal on d Ratio d. sächs Gesellsch. d Scientific. Leipzig, p.303 -310 ( 1921).
  • About the roots trinomischer equations, Ber. royal on d Ratio d. sächs Gesellsch. d Scientific. Leipzig, pp. 3-8 (1922 ).
  • About the orbit determination of comets and planets, Encyclopedia of mathem.Wissenschaften 1906
  • About the analytic continuation of certain Dirichlet series, Mathematische Annalen in 1905
  • About the calculation of retarded potentials, news Göttingen Akad.1904
  • For electron theory, news Göttingen Akad.1903
  • About the integral equations of the electron theory, Mathem.Annalen 1908
  • The determination of a line element in normal coordinates of the Riemann curvature tensor, Mathem.Annalen 1925
  • The Green's function of the wave equation for a wedge- shaped boundary, Mathem.Annalen 1951/2, the classical Sommerfeld solution of the diffraction on the wedge
Volary Hans Hahn (mathematician) Heinrich Franz Friedrich Tietze (433) Eros Carl David Tolmé Runge Convex set Neue Deutsche Biographie Integrated Authority File
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