Mathematische Annalen

, Volume 103, Issue 1, pp 52–69

A generalization of the sturm separation and comparison theorems inn-space

  • Marston Morse


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  1. 3).
    We adopt the convention that a repetition of a subscript in a term shall indicate a sum with respect to that subscript.Google Scholar
  2. 4).
    See Davis R. D., The inverse problem of the calculus of variations in higher space, Transactions of the American Mathematical Society30 (1928), p. 711–713.Google Scholar
  3. 5).
    See Hadamard, Leçons sur le calcul des variations, Paris 1910,1, p. 319.Google Scholar
  4. 6).
    See Bolza, Vorlesungen über Variationsrechnung, p. 626.Google Scholar
  5. 7).
    The nullity of a determinant is its order minus its rank.Google Scholar
  6. 8).
    Ann-manifoldS is called regular if on it the coordinates of points neighring a given point admit a representation in terms ofn parameters in which not all of the jacobians of the coordinates with respect to then parameters are zero.Google Scholar
  7. 9).
    Bliss, The transformations of Clebsch in the calculus of variations, Transactions of the American Mathematical Society17 (1916), p. 595.Google Scholar
  8. 10).
    By the positive and negative type numbers of a real quadratic form, will be understood the number of positive and negative terms respectively in the form when reduced by a real non-singular linear transformation to squared terms only.Google Scholar

Copyright information

© Springer-Verlag 1930

Authors and Affiliations

  • Marston Morse
    • 1
  1. 1.CambridgeUSA

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