Gustav Herglotz

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Gustav Herglotz
Gustav Herglotz.jpeg
Born (1881-02-02)2 February 1881
Wallern, Bohemia, Austro-Hungarian Empire
Died 22 March 1953(1953-03-22) (aged 72)
Göttingen, Lower Saxony
Nationality German
Alma mater University of Göttingen
LMU Munich
Known for Works in seismology
Scientific career
Fields Mathematics
Institutions University of Leipzig
Doctoral advisor Hugo von Seeliger
Ludwig Boltzmann
Doctoral students Emil Artin
Felix Burkhardt
Peter Scherk

Gustav Herglotz (2 February 1881 – 22 March 1953) was a German Bohemian mathematician. He is best known for his works on the theory of relativity and seismology.

Biography[edit]

Herglotz studied Mathematics and Astronomy at the University of Vienna in 1899, and attended lectures by Ludwig Boltzmann. In this time of study, he had a friendship with his colleagues Paul Ehrenfest, Hans Hahn and Heinrich Tietze. In 1900 he went to the LMU Munich and achieved his Doctorate in 1902 under Hugo von Seeliger. Afterwards, he went to the University of Göttingen, where he habilitated under Felix Klein. In 1904 he became Privatdozent for Astronomy and Mathematics there, and in 1907 Professor extraordinarius. In 1908 he became Professor extraordinarius in Vienna, and in 1909 at the University of Leipzig. From 1925 (until becoming Emeritus in 1947) he again was in Göttingen as the successor of Carl Runge on the chair of applied mathematics. One of his students was Emil Artin.

Work[edit]

Herglotz worked in the fields of seismology, number theory, celestial mechanics, theory of electrons, special relativity, general relativity, hydrodynamics, refraction theory.

  • In 1907,[3] he became interested in the theory of earthquakes, and together with Emil Wiechert, he developed the Wiechert–Herglotz method for the determination of the velocity distribution of Earth's interior from the known propagation times of seismic waves (an inverse problem). There, Herglotz solved a special integral equation of Abelian type.
The theorem also asserts that the probability measure is unique to f.

Selected works[edit]

  • Gesammelte Schriften / Gustav Herglotz, edited for d. Akad. d. Wiss. in Göttingen by Hans Schwerdtfeger. XL, 652 p., Vandenhoeck & Ruprecht, Göttingen 1979, ISBN 3-525-40720-3.[10]
  • Vorlesungen über die Mechanik der Kontinua / G. Herglotz, prepared by R. B. Guenther and H. Schwerdtfeger, Teubner-Archiv zur Mathematik; vol. 3, 251 p.: 1 Ill., graph. Darst.; 22 cm, Teubner, Leipzig 1985.
  • Über die analytische Fortsetzung des Potentials ins Innere der anziehenden Massen, Preisschriften der Fürstlichen Jablonowskischen Gesellschaft zu Leipzig, VII, 52 pages, with 18 Fig.; Teubner, Leipzig (1914).[11]
  • Über das quadratische Reziprozitätsgesetz in imaginären quadratischen Zahlkörpern, Ber. über d. Verh. d. königl. sächs. Gesellsch. d. Wissensch. zu Leipzig, pp. 303–310 (1921).

See also[edit]

References[edit]

  1. ^ Herglotz, Gustav (1904). "Über die Berechnung retardierter Potentiale". Gött. Nachr. (6): 549 – 556. 
  2. ^ Sommerfeld, Arnold (1910). "Zur Relativitätstheorie II: Vierdimensionale Vektoranalysis" [Wikisource translation: On the Theory of Relativity II: Four-dimensional Vector Analysis]. Annalen der Physik. 338 (14): 649–689. Bibcode:1910AnP...338..649S. doi:10.1002/andp.19103381402. 
  3. ^ Herglotz, Gustav (1907), "Über das Benndorfsche Problem der Fortpflanzungsgeschwindigkeit der Erdbebenstrahlen", Physikalische Zeitschrift, 8: 145–147 
  4. ^ Herglotz, Gustav (1910) [1909], "Über den vom Standpunkt des Relativitätsprinzips aus als starr zu bezeichnenden Körper" [Wikisource translation: On bodies that are to be designated as "rigid" from the standpoint of the relativity principle], Annalen der Physik, 336 (2): 393–415, Bibcode:1910AnP...336..393H, doi:10.1002/andp.19103360208 
  5. ^ Herglotz, G. (1911), "Über Potenzreihen mit positivem, reellen Teil im Einheitskreis", Ber. Verh. Sachs. Akad. Wiss. Leipzig, 63: 501–511 
  6. ^ Jim Agler, John Harland, and Benjamin J. Raphael (2008) Classical Function Theory, Operator Dilation Theory, and Machine Computations on Multiply-Connected Domains, Memoirs of the American Mathematical Society #892, ISSN 0065-9266
  7. ^ Herglotz, Gustav (1911), "Über die Mechanik des deformierbaren Körpers vom Standpunkte der Relativitätstheorie", Annalen der Physik, 341 (13): 493–533, Bibcode:1911AnP...341..493H, doi:10.1002/andp.19113411303 ; English translation by David Delphenich: On the mechanics of deformable bodies from the standpoint of relativity theory.
  8. ^ a b Pauli, Wolfgang (1921), "Die Relativitätstheorie", Encyclopädie der mathematischen Wissenschaften, 5 (2): 539–776 
    In English: Pauli, W. (1981) [1921]. Theory of Relativity. Fundamental Theories of Physics. 165. Dover Publications. ISBN 0-486-64152-X. 
  9. ^ G. Herglotz, Zur Einsteinschen Gravitationstheorie, Ber. über d. Verh. d. königl. sächs. Gesellsch. d. Wissensch. zu Leipzig, pp. 199–203 (1916).
  10. ^ Bochner, Salomon (1979). "Review: Gesammelte Schriften, by Gustav Herglotz" (PDF). Bull. Amer. Math. Soc. (N.S.). 1 (6): 1020–1022. doi:10.1090/s0273-0979-1979-14724-4. 
  11. ^ Longley, W. R. (1916). "Review: Ueber die analytische Fortsetzung des Potentials ins Innere der anziehenden Massen, by Gustav Herglotz" (PDF). Bull. Amer. Math. Soc. 22 (7): 361–364. doi:10.1090/s0002-9904-1916-02805-9. 

External links[edit]