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On the de Branges weight functions

Summary: We find new representations of the derivatives of the weight functions used by de Branges in his proof of the Milin, Robertson and Bieberbach conjectures.
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On Walsh functions with respect to weights.

Summary: The orthogonal polynomials are constructed from the power functions by means of the Schmidt orthogonalization process in which the scalar product is generated by weight functions. There is another general construction with probabilistic method in the background that can be applied to obtain orthogonal and biorthogonal systems.
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