A decomposition technique of the solution of an n-th order linear differential equation into a set of solutions of 2-nd order linear differential equations is presented.
This paper contains some results for algebraic polynomials in the complex plane involving the polar derivative that are inspired by some classical results of Bernstein. Obtained results yield the polar derivative analogues of some inequalities giving estimates for the growth of derivative of lacunary polynomials.
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A new approach to the study of zeros of orthogonal polynomials with respect to an Hermitian and regular linear functional is presented. Some results concerning zeros of kernels are given.
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