A conjecture of Schoenberg
| Autor: | Ivanov KG, Sharma A, de Bruin MG |
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| Jazyk: | angličtina |
| Rok vydání: | 1999 |
| Předmět: | |
| Zdroj: | Journal of Inequalities and Applications, Vol 1999, Iss 3, p 838171 (1999) |
| Druh dokumentu: | article |
| ISSN: | 1025-5834 1029-242X |
| Popis: | For an arbitrary polynomial with the sum of all zeros equal to zero, , the quadratic mean radius is defined by Schoenberg conjectured that the quadratic mean radii of and satisfy where equality holds if and only if the zeros all lie on a straight line through the origin in the complex plane (this includes the simple case when all zeros are real) and proved this conjecture for and for polynomials of the form . It is the purpose of this paper to prove the conjecture for three other classes of polynomials. One of these classes reduces for a special choice of the parameters to a previous extension due to the second and third authors. |
| Databáze: | Directory of Open Access Journals |
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