Advertisement

Matrices of infinite order

  • C. C. Mac Duffee
Chapter
  • 358 Downloads
Part of the Ergebnisse der Mathematik und Ihrer Grenƶgebiete book series (MATHE1, volume 5)

Abstract

Infinite determinants. The concept of infinite determinant was introduced by G. W. Hill 5 in connection with the solution of differential equations.

Keywords

Quadratic Form Finite Order Orthogonal Transformation Infinite Order FREDHOLM Determinant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

  1. 1.
    Schlesinger, L.: J. reine angew. Math. Vol. 128 (1904) pp. 263–297.Google Scholar
  2. 2.
    Schlesinger, L.: Math. Z. Vol. 33 (1931) pp. 33–61.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Turnbull, H. W.: Proc. Edinburgh Math. Soc. II Vol. 1 (1927) pp. 111–128.CrossRefGoogle Scholar
  4. 4.
    Loewy, A.: Math. Ann. Vol. 78 (1918) pp. 1–51, 343-358 and 359-368.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hill, G. W.: Acta math. Vol. 8 (1886) pp. 1–36.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 1.
    Poincaré: Bull. Soc. Math. France Vol. 14 (1886) pp. 77–90.MathSciNetGoogle Scholar
  7. 2.
    Koch, H. Von: Acta math. Vol. 15 (1891) pp. 53–63.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Koch, H. Von: Acta math. Vol. 16 (1892–1893) pp. 217–295.MathSciNetzbMATHCrossRefGoogle Scholar
  9. Koch, H. Von: C. R. Acad. Sei., Paris Vol. 116 (1893) pp. 91–93.zbMATHGoogle Scholar
  10. Koch, H. Von: Rend. Circ. mat. Palermo Vol. 28 (1909) pp. 255–266.CrossRefGoogle Scholar
  11. 3.
    Bôbr, ST.: Math. Z. Vol. 10 (1921) pp. 1–11.CrossRefGoogle Scholar
  12. 4.
    Cohen, L. W: Bull. Amer. Math. Soc. Vol. 36 (1930) pp. 563–572.MathSciNetzbMATHCrossRefGoogle Scholar
  13. 5.
    Schmidt, E.: Rend. Circ. mat. Palermo Vol. 25 (1908) pp. 53–77.zbMATHCrossRefGoogle Scholar
  14. 6.
    Toeplitz: Rend. Circ. mat. Palermo Vol. 28 (1909) pp. 88–96.zbMATHCrossRefGoogle Scholar
  15. 7.
    Wintner: Math. Z. Vol. 24 (1925) p. 266.MathSciNetzbMATHCrossRefGoogle Scholar
  16. 8.
    Stieltjes, T. J.: Ann. Fac. Sci. Univ. Toulouse Vol. 8 (1894) J1–J122.MathSciNetGoogle Scholar
  17. 9.
    VonKoch: C. R. Acad. Sci., Paris Vol. 120 (1895) pp. 144–147.Google Scholar
  18. 13.
    Hellinger and Toeplitz: Knzykl. der math. Wiss. II C 13 § 17 (1927)Google Scholar
  19. 1.
    Gillespie, D, C.: Bull. Amer. Math. Soc. Vol. 33 (1927) pp. 654–655, abstract only.zbMATHGoogle Scholar
  20. 2.
    Shaw, A. A.: Amer. Math. Monthly Vol. 38 (1931) pp. 188–194.MathSciNetCrossRefGoogle Scholar
  21. 1.
    Hellinger and Toeplitz: Math. Ann. Vol. 69 (1910) pp. 289–330.MathSciNetzbMATHCrossRefGoogle Scholar
  22. 1.
    Toeplitz: Math. Ann. Vol. 70 (1910) pp. 351–376.MathSciNetCrossRefGoogle Scholar
  23. 2.
    Hellinger and Toeplitz: Math. Ann. Vol. 69 (1910) pp. 289–330.MathSciNetzbMATHCrossRefGoogle Scholar
  24. 4.
    Hahn, H.: Mh. Math. Phys. Vol. 23 (1912) pp. 161–224.zbMATHGoogle Scholar
  25. 5.
    Murray, F. H.: Ann. of Math. Vol. 29 (1928) pp. 133–139.Google Scholar
  26. 6.
    Hyslop, J.: Proc. London Math. Soc. II Vol. 24 (1926) pp. 264–304.CrossRefGoogle Scholar
  27. 7.
    Schur, I.: Math. Z. Vol. 1 (1918) pp. 184–207.MathSciNetCrossRefGoogle Scholar
  28. 8.
    Wintner, A.: Amer. J. Math. Vol. 54 (1932) pp. 145–149.MathSciNetzbMATHCrossRefGoogle Scholar
  29. 9.
    Martin, M. H.: Amer. J. Math. Vol. 54 (1932) pp. 579–631.MathSciNetCrossRefGoogle Scholar
  30. 11.
    Neumann, J. Von: J. reine angew. Math. Vol. 161 (1929) pp. 208–236.zbMATHGoogle Scholar
  31. Neumann, J. Von: Math. Ann. Vol. 102 (1929) pp. 49–131.zbMATHCrossRefGoogle Scholar
  32. 1.
    Dirac, P. A. M.: Proc. Cambridge Phil. Soc. Vol. 23 (1926) pp. 412–418.zbMATHCrossRefGoogle Scholar
  33. 3.
    Volterra, V.: Atti Accad. naz. Lincei, Rend. V Vol. 19 (1910) pp. 169–180.zbMATHGoogle Scholar
  34. 5.
    Dirac, P. A. M.: Proc. Roy. Soc. London A Vol. 113 (1926–1927) pp. 621 to 641.Google Scholar
  35. 6.
    Michal, A. D.: Amer. J. Math. Vol. 50 (1928) pp. 473–517.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1933

Authors and Affiliations

  • C. C. Mac Duffee

There are no affiliations available

Personalised recommendations