Polinomial Zeros According to the Haar-Type System

We obtained an accurate estimate for the Lebesgue measure of the polynomial zeros set of arbitrarily large order with nonzero coefficients according to the generalized Haar system for the case of a bounded sequence of parameters defining a given system. Similar problems were investigated for the case of an unbounded sequence of parameters of the generalized Haar system. In the latter case it is shown that there is always a polynomial, whose Lebesgue measure of the polynomial zeros set has an arbitrarily small difference from one.

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