Abstract
Representation theorems for Tchebycheff polynomials with homogeneous boundary conditions are proved, and a number of extremal problems are solved.
Similar content being viewed by others
References
F. R. Gantmacher and M. G. Krein,Oscillatory Matrices and Kernels and Small Vibrations of Mechanical Systems, (in Russian), 2nd ed., Moscow, 1950.
S. Karlin,Representation theorems for positive functions, J. Math. Mech.12 (1963), 559–618.
S. Karlin,Generalized Bernstein inequalities, Acta Sci. Math. (Szeged), (1966), pp. 1–15.
S. Karlin,Total Positivity, Stanford Univ. Press, Stanford, Calif., 1968.
S. Karlin,Total positivity, interpolation by splines, and Green’s functions of differential operators, J. Approximation Theory4 (1971), 91–112.
S. Karlin and J. Karon,On Hermite-Birkhoff interpolation, J. Approximation Theory6 (1972), 90–115.
S. Karlin and C. A. Micchelli,The fundamental theorem of algebra for monosplines statisfying boundary conditions, Israel J. Math.11 (1972), 405–451.
S. Karlin and L. S. Shapley,Geometry of moment spaces, Mem. Amer. Math. Soc.12 (1953).
S. Karlin and W. Studden,Tchebycheff Systems: with Applications in Analysis and Statistics, Interscience, New York, 1966.
C. A. Micchelli and T. J. Rivlin,Quadrature formulae and Hermite-Birkhoff interpolation, IBM J. Res. Develop., RC 3396, June, 1971.
M. A. Neumark,Lineare Differentialoperatoren, Akademie-Verlag, Berlin, 1960.
I. J. Schoenberg,On Hermite-Birkhoff interpolation, J. Math. Anal. Appl.16 (1966), 538–543.
G. Szegö,Orthogonal Polynomials, Amer. Math. Soc., Vol. XXIII, New York, 1969.
Author information
Authors and Affiliations
Additional information
This work is part of the author’s doctoral thesis under the supervision of Professor S. Karlin.
Rights and permissions
About this article
Cite this article
Pinkus, A. Representation theorems for Tchebycheffian polynomials with boundary conditions and their applications. Israel J. Math. 17, 11–34 (1974). https://doi.org/10.1007/BF02756821
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02756821