References
M. Berger, P. Gauduchon and E. Mazet,Le Spectre d'une Variété Riemannienne, Springer-Verlag, 1971.
R. Courant and D Hilbert,Methods of Mathematical Physics, I and II, Inter-Science Publishers, 1962.
N. Dunford and J. T. Schwarz,Linear Operators, I and II, Interscience Publishers, 1967.
K. Fan,On a theorem of Weyl concerning eigenvalues of linear transformations, Proc. Nat. Acad. Sci. 35 (1949), 625–26.
S. Friedland,Extremal eigenvalue problems for convex sets of symmetric matrices and operators, Israel J. Math. 15 (1973) 311–331.
S. Friedland,Extremal eigenvalue problems defined for certain classes of functions and measures, 1975, Preprint, Institute for Advanced Study.
—,Inverse eigenvalue problems, Linear Algebra Appl. 17 (1977), 15–51.
S. Friedland,Extremal eigenvalue problems defined for certain classes of functions, J. Ratl. Mech. and Anal. to appear.
S. Friedland,Extremal eigenvalue problems defined on conformals classes of compact Riemannian manifolds, to appear.
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.
J. Hersch,Quatre propriétés isopérimétriques de mambrane spheriques homogènes. C. R. Acad. Sc. Paris 270 (1971), 1645–1648.
S. Karlin and W. J. Studden,Tchebycheff with Applications in Analysis and Statistics, Interscience Publishers, 1966.
S. Karlin,Total Positivity, Stanford University Press, 1968.
—,Some extremal problems for eigenvalues of certain matrix and integral operators, Advances in Math. 9 (1972), 93–136.
T. Kato,Perturbation Theory for Linear Operators, Springer-Verlag, 1966.
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.
P. Nowosad,Isoperimetric eigenvalue problems in algebra, Comm. Pure Appl. Math. 21 (1968), 410–465.
P. Nowosad,Characterization of extremal eigenvalues for certain differential operator, Tech. Report M.R.C., Univ. of Wisconsin 1970.
P. Nowosad,Operadores positivos e otimização à engenharia nuclear, São Paulo, 1977.
G. Pólya and M. Schiffer,Convexity of functionals by transplantation, J. Analyse Math. 3 (1953/54).
G. Pólya and G. Szegö,Isoperimetric Inequalities in Mathemathical Physics, Princeton Univ., 1951.
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Friedland, S. Extremal eigenvalue problems. Bol. Soc. Bras. Mat 9, 13–40 (1978). https://doi.org/10.1007/BF02584790
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DOI: https://doi.org/10.1007/BF02584790