Pacific Journal of Mathematics

Applications of the theory of quadratic forms in Hilbert space to the calculus of variations.

Magnus R. Hestenes

Article information

Source
Pacific J. Math., Volume 1, Number 4 (1951), 525-581.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103052021

Mathematical Reviews number (MathSciNet)
MR0046590

Zentralblatt MATH identifier
0045.20806

Subjects
Primary: 49.0X

Citation

Hestenes, Magnus R. Applications of the theory of quadratic forms in Hilbert space to the calculus of variations. Pacific J. Math. 1 (1951), no. 4, 525--581. https://projecteuclid.org/euclid.pjm/1103052021


Export citation

References

  • [1] A. A. Albert, A quadratic form problem in the calculus of variations, Bull. Amer. Math. Soc. 44 (1938), 250-252.
  • [2] G. D. Birkhoff and M. R. Hestenes, Natural isoperimetric conditions in the calculus of variations, Duke Math. J. 1 (1935), 198-286.
  • [3] G. A. Bliss, A boundary value problem for a systemof ordinary differentialequa- tions of the first order, Trans. Amer. Math. Soc. 28 (1926), 561-584.
  • [4] G. A. Bliss, Lectures on the calculus of variations, The University of Chicago Press, 1946.
  • [5] J. W. Calkin, Functions of several variables and absolute continuity I, Duke Math. J. 6 (1940), 170-186.
  • [6] L. M. Graves, The Weierstrass condition for multiple integral variation problems, Duke Math. J. 5 (1939), 656-660.
  • [7] K. Hazard, Index theorems for the problem of Bolza in the calculus of variations, Contributions to the calculus of variations, 1938-1941, The University of Chicago Press, pp. 293-356.
  • [8] M. R. Hestenes, Sufficient conditions for multiple integral problems in the calculus of variations, Amer. J. Math. 70 (1948),239-275.
  • [9] M. R. Hestenes and E. J. McShane, A theorem on quadratic forms and its application in the calculus of variations, Trans. Amer. Math. Soc. 47 (1940),501-512.
  • [10] W. Karush, Isoperimetric problems and index theorems in the calculus of variations, Dissertation, The University of Chicago, 1942.
  • [11] C. B. Morrey, Jr., Functionsof several variables and absolute continuity //, Duke Math. J. 6 (1940), 187-215.
  • [12] C. B. Morrey, Multiple integral problems in the calculus of variations and related topics, University of California Publications in Mathematics, New Series, 1 (1943), 1-130.
  • [13] M. Morse, The calculus of variations in the large, American Mathematical Society Colloquium Publications, vol.18, New York, 1934.
  • [14] W.T. Reid, Boundary value problems of the calculus of variations, Bull. Amer. Math. Soc. 43 (1937), 633-666.
  • [15] W.T. Reid, A new class of self-adjoint boundary value problems, Trans. Amer. Math. Soc. 52 (1942), 381-425.
  • [16] W.T. Reid, A theorem on quadratic forms, Bull. Amer, Math. Soc. 44 (1938), 437-440.
  • [17] L. Ritcey, Index theorems for discontinuous problems in the calculus of variations, Dissertation, The University of Chicago, 1945.
  • [18] M. H. Stone, Transformations in Hilbert space and their applications toanalysis, American Mathematical Society Colloquium Publications, vol.15, New York, 1932.
  • [19] Bela v. Sz.-Nagy, Spektraldarstellunglinearer Transformationen des Hilbertschen Raumes, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol.5, part 5, Springer, Berlin, 1942.
  • [20] F. J. Terpstra, Die Darstellung biquadratischer Formen als Summen von Quadraten mit Anwendung auf die Variationsrechnung, Math. Ann. 116 (1939), 166-180.