Bounded point evaluations and polynomial approximation

Thomson, James E.

doi:10.1090/S0002-9939-1995-1242106-1

Bounded point evaluations and polynomial approximation
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by James E. Thomson PDF

Proc. Amer. Math. Soc. 123 (1995), 1757-1761 Request permission

Abstract:

We consider the set of bounded point evaluations for polynomials with respect to the ${L^P}$-norm for a measure. We give an example of a measure where the corresponding sets of bounded point evaluations vary with the exponent p. The main ingredient is the remarkable work of K. Seip on interpolating and sampling sequences for weighted Bergman spaces.

References

John Akeroyd, Polynomial approximation in the mean with respect to harmonic measure on crescents, Trans. Amer. Math. Soc. 303 (1987), no. 1, 193–199. MR 896016, DOI 10.1090/S0002-9947-1987-0896016-X
James E. Brennan, Invariant subspaces and weighted polynomial approximation, Ark. Mat. 11 (1973), 167–189. MR 350398, DOI 10.1007/BF02388514
John B. Conway, The theory of subnormal operators, Mathematical Surveys and Monographs, vol. 36, American Mathematical Society, Providence, RI, 1991. MR 1112128, DOI 10.1090/surv/036
William W. Hastings, A construction of Hilbert spaces of analytic functions, Proc. Amer. Math. Soc. 74 (1979), no. 2, 295–298. MR 524303, DOI 10.1090/S0002-9939-1979-0524303-4
S. N. Mergeljan, On the completeness of systems of analytic functions, Amer. Math. Soc. Transl. (2) 19 (1962), 109–166. MR 0131561, DOI 10.1090/trans2/019/04
Kristian Seip, Regular sets of sampling and interpolation for weighted Bergman spaces, Proc. Amer. Math. Soc. 117 (1993), no. 1, 213–220. MR 1111222, DOI 10.1090/S0002-9939-1993-1111222-5
Kristian Seip, Beurling type density theorems in the unit disk, Invent. Math. 113 (1993), no. 1, 21–39. MR 1223222, DOI 10.1007/BF01244300
James E. Thomson, Approximation in the mean by polynomials, Ann. of Math. (2) 133 (1991), no. 3, 477–507. MR 1109351, DOI 10.2307/2944317