Inequalities for polynomial zeros. (English) Zbl 1029.26005
Rassias, Themistocles M. (ed.), Survey on classical inequalities. Dordrecht: Kluwer Academic Publishers. Math. Appl., Dordr. 517, 165-202 (2000).
In the first part of this survey paper one may find various bounds for the moduli of zeros of univariate polynomials. These bounds are expressed as functions of the coefficients of the standard (monomial) expansion. The second part is devoted to the location of zeros in terms of the coefficients of an orthogonal expansion. In particular, there are recorded estimates for strips containing all the zeros.
For the entire collection see [Zbl 0998.00010].
For the entire collection see [Zbl 0998.00010].
Reviewer: Mihai Cipu (Bucureşti)
MSC:
| 26C10 | Real polynomials: location of zeros |
| 26D05 | Inequalities for trigonometric functions and polynomials |
| 30C10 | Polynomials and rational functions of one complex variable |
| 30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 30A10 | Inequalities in the complex plane |
| 15A42 | Inequalities involving eigenvalues and eigenvectors |
| 15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |
