Pacific Journal of Mathematics

On the location of the zeros of some infrapolynomials with prescribed coefficients.

O. Shisha and J. L. Walsh

Article information

Source
Pacific J. Math., Volume 14, Number 3 (1964), 1103-1109.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103034003

Mathematical Reviews number (MathSciNet)
MR0169991

Zentralblatt MATH identifier
0144.07102

Subjects
Primary: 30.11

Citation

Walsh, J. L.; Shisha, O. On the location of the zeros of some infrapolynomials with prescribed coefficients. Pacific J. Math. 14 (1964), no. 3, 1103--1109. https://projecteuclid.org/euclid.pjm/1103034003


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References

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  • [2] M. Fekete. 1951. On the structure of extremal polynomials, Proc. Nat'l. Acad. Sci. U. S. 37, pp. 95-103.
  • [3] M. Fekete and J. L. von Neumann. 1922. Uber die Lage der Nullstellengewisser Minimumpolynome,Jber. Deutsch. Math. Verein. 31, pp. 125-138.
  • [4] M. Fekete and J. L. Walsh. 1957. On restricted infrapolynomials,J. Analyse Math.
  • [5] M. Marden. 1949. On the zeros of rational functions having prescribed poles, with applications to the derivative of an entire function of finite genre, Trans. Amer. Math. Soc. 66, pp. 407-418.
  • [6] O. Shisha. 1962. An extension of Jensen's theorem for the derivative of a polynomial and for infrapolynomials,J. of Res. of the Nat'l. Bur. of Standards, 66B, pp. 53-55.
  • [7] O. Shisha and J. L. Walsh. 1961. The zeros of infrapolynomials with some prescribed coefficients, J. Analyse Math. 9, pp. 111-160.
  • [8] J. L. Walsh. 1922. On the location of the roots of certain types of polynomials, Trans. Amer. Math. Soc. 24, pp. 163-180.
  • [9] J. L. Walsh. 1922. On the location of the roots of certain types of polynomials, 1950. The location of critical points of analytic and harmonicfunctions, Colloquium Publications, Amer. Math. Soc. 34.
  • [10] J. L. Walsh. 1922. On the location of the roots of certain types of polynomials, 1958. On infrapolynomialswith prescribed constant term, J. Math. Pures Appl. 37, pp. 295-316.
  • [11] J. L. Walsh and O. Shisha. 1963. The zeros of infrapolynomialswith prescribed values at given points, Proc. Amer. Math. Soc, 14, pp. 839-844.
  • [12] J. L. Walsh and M. Zedek. 1956. On generalized Tchebycheff polynomials, Proc. Nat'l. Acad. Sci. U. S. 42, pp. 99-104.
  • [13] M. Zedek. 1955. Fejer's theorem on the zeros of extremal polynomialsgeneralized. Preliminary report. Bull. Amer. Math. Soc. 61, p. 49.