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**1 - 3**of**3**### An orthogonal polynomial sequence

"... Abstract. We show a weak analogon of Bochner’s theorem for polynomial hypergroups. We examine which assumptions are necessary to regain some of the statements of the original theorem. We conclude that orthogonality and nonnegativity are not crucial for the theorem. In order to show one of our result ..."

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Abstract. We show a weak analogon of Bochner’s theorem for polynomial hypergroups. We examine which assumptions are necessary to regain some of the statements of the original theorem. We conclude that orthogonality and nonnegativity are not crucial for the theorem. In order to show one of our results, we provide a polynomial inequality, which characterizes the size of the set where a real polynomial on the real line is bounded by some constant