On the spans of polynomials and their derivatives |
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Authors: | Rajesh Pereira |
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Institution: | University of Saskatchewan, Saskatoon SK, Canada S7N 5E6 |
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Abstract: | We prove that a majorization-type relation among the root sets of three polynomials implies that the same relation holds for the root sets of their derivatives. We then use this result to give a unified derivation of the classical results due to Sz.-Nagy, Robinson, Meir and Sharma which relate the span of a polynomial to the spans of its first or higher derivatives. We also show how this relation can be generated by interlacing polynomials. |
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Keywords: | Spans of polynomials Differentiators Geometry of polynomials Majorization order Interlacing |
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