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We obtain a necessary and sufficient condition for the lacunary polynomials to be dense in weighted L p spaces of functions on the real line. This generalizes the solution to the classical Bernstein problem given by Izumi, Kawata and Hall.
and Applied Analysis 3 for any potential a · ≥ 0. The “inverse” inequality in some sense is much more elaborate. When D is a bounded domain in R, Cranston see 8 , the case n 2 is implicitly contained in 9 have proved that GaD ·, · ≥ M D GD ·, · , 1.6 where M D M D, a is a positive constant and independent of points in D. If a 0, then obviously M D ≡ 1.… (More)