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The method of symmetric and Hermitian forms in the theory of separation of the roots of algebraic equations. (English) Zbl 0584.12018
Summary: The present publication (translated from the Russian by O. Boshko and J. L. Howland) is in the nature of a survey; therefore the presentation is similar to articles in mathematical encyclopedias. We do not intend to give a systematic presentation of all relevant problems on the basis of some single method, but rather attempt to include different methods of establishing the various propositions, indicating their characteristic differences.
All basic methods and results are presented in detail; moreover, the indications given in the paper will allow a more or less experienced mathematician to construct proofs by himself of nearly all the results given.
Section headings: 1. The Hermite-Jacobi method; 2. The fundamental properties and applications of Bezoutiants; 3. The Hermite method for the separation of complex roots and its development; 4. Association with some problems of function theory.

MSC:
12D05 Polynomials in real and complex fields: factorization
15A63 Quadratic and bilinear forms, inner products
12E12 Equations in general fields
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
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