Extremal eigenvalue problems

  • Shmuel Friedland
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. Berger, P. Gauduchon and E. Mazet,Le Spectre d'une Variété Riemannienne, Springer-Verlag, 1971.Google Scholar
  2. [2]
    R. Courant and D Hilbert,Methods of Mathematical Physics, I and II, Inter-Science Publishers, 1962.Google Scholar
  3. [3]
    N. Dunford and J. T. Schwarz,Linear Operators, I and II, Interscience Publishers, 1967.Google Scholar
  4. [4]
    K. Fan,On a theorem of Weyl concerning eigenvalues of linear transformations, Proc. Nat. Acad. Sci. 35 (1949), 625–26.CrossRefGoogle Scholar
  5. [5]
    S. Friedland,Extremal eigenvalue problems for convex sets of symmetric matrices and operators, Israel J. Math. 15 (1973) 311–331.MATHMathSciNetGoogle Scholar
  6. [6]
    S. Friedland,Extremal eigenvalue problems defined for certain classes of functions and measures, 1975, Preprint, Institute for Advanced Study.Google Scholar
  7. [7]
    —,Inverse eigenvalue problems, Linear Algebra Appl. 17 (1977), 15–51.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    S. Friedland,Extremal eigenvalue problems defined for certain classes of functions, J. Ratl. Mech. and Anal. to appear.Google Scholar
  9. [9]
    S. Friedland,Extremal eigenvalue problems defined on conformals classes of compact Riemannian manifolds, to appear.Google Scholar
  10. [10]
    S. Friedland and W. K. Hayman,Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions. Comment. Math. Halvetici 51 (1976), 133–161.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    J. Hersch,Quatre propriétés isopérimétriques de mambrane spheriques homogènes. C. R. Acad. Sc. Paris 270 (1971), 1645–1648.MathSciNetGoogle Scholar
  12. [12]
    S. Karlin and W. J. Studden,Tchebycheff with Applications in Analysis and Statistics, Interscience Publishers, 1966.Google Scholar
  13. [13]
    S. Karlin,Total Positivity, Stanford University Press, 1968.Google Scholar
  14. [14]
    —,Some extremal problems for eigenvalues of certain matrix and integral operators, Advances in Math. 9 (1972), 93–136.MATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    T. Kato,Perturbation Theory for Linear Operators, Springer-Verlag, 1966.Google Scholar
  16. [16]
    M. G. Krein,On certain problems on the maximum and minimum of characteristic values and on the Lyapunov zones of stability. Trans. Amer. Math. Soc. Ser. 2, Vol. 1 (1955), 163–187.MathSciNetGoogle Scholar
  17. [17]
    P. Nowosad,Isoperimetric eigenvalue problems in algebra, Comm. Pure Appl. Math. 21 (1968), 410–465.MathSciNetGoogle Scholar
  18. [18]
    P. Nowosad,Characterization of extremal eigenvalues for certain differential operator, Tech. Report M.R.C., Univ. of Wisconsin 1970.Google Scholar
  19. [19]
    P. Nowosad,Operadores positivos e otimização à engenharia nuclear, São Paulo, 1977.Google Scholar
  20. [20]
    G. Pólya and M. Schiffer,Convexity of functionals by transplantation, J. Analyse Math. 3 (1953/54).Google Scholar
  21. [21]
    G. Pólya and G. Szegö,Isoperimetric Inequalities in Mathemathical Physics, Princeton Univ., 1951.Google Scholar

Copyright information

© Sociedade Brasileira de Matemática 1978

Authors and Affiliations

  • Shmuel Friedland
    • 1
  1. 1.Institute of MathematicsThe Hebrew UniversityJerusalem

Personalised recommendations