On the Coincidence Theorem
Copyright policy )On the Coincidence Theorem
We are proving Coincidence theorem due to Walsh for the case when the total degree of a polynomial is less than the number of arguments. Also, the following result has been proven: if $$p(z)$$ is a complex polynomial of degree $$n$$, then closed disk D that contains at least $$n-1$$ of its zeros (counting multiplicity) contains at least $$\left[\frac{n-2k+1}{2} \right]$$ zeros of its $$k$$-th derivative, provided that the arithmetical mean of these zeros is also centre of D. We also prove a variation of the classical composition theorem due to Szegö.
- University of Belgrade Serbia
apolar polynomials, critical points of a polynomial, zeros of polynomials, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), coincidence theorem
apolar polynomials, critical points of a polynomial, zeros of polynomials, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), coincidence theorem
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