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Mean-square approximation by polynomials on the unit disk

1990
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Transactions of the American Mathematical Society
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We investigate p2(fJ) , the closure in L2(fJ) of the complex polynomials, for certain measures fJ on the closed unit disk in the complex plane. Specifically, we present a condition on fJ which guarantees that p2(fJ) decomposes into a natural direct sum. 1 il-J log log G(r) dr (some small J). Let us always use the term arc to mean a non empty open arc in {) D . Theorem D. Suppose the integral (1.2) converges (and G satisfies a mild regularity condition). If log W ELI (I) for some arc I c {)D,

doi:10.1090/s0002-9947-1990-0948193-x
fatcat:4smuft7kizf7nf4udp6snmz224