Pick and peak interpolation

Izzo, Alexander

doi:10.1090/proc/13755

Pick and peak interpolation
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by Alexander J. Izzo PDF

Proc. Amer. Math. Soc. 146 (2018), 717-721 Request permission

Abstract:

We show how Pick interpolation and interpolation on peak interpolation sets can be combined in an abstract uniform algebra setting. In particular, as a special case, the Rudin-Carleson theorem can be combined with the classical Pick interpolation theorem on the disc.

References

Lennart Carleson, Representations of continuous functions, Math. Z. 66 (1957), 447–451. MR 84035, DOI 10.1007/BF01186621
Brian Cole, Keith Lewis, and John Wermer, Pick conditions on a uniform algebra and von Neumann inequalities, J. Funct. Anal. 107 (1992), no. 2, 235–254. MR 1172022, DOI 10.1016/0022-1236(92)90105-R
Brian J. Cole and John Wermer, Pick interpolation, von Neumann inequalities, and hyperconvex sets, Complex potential theory (Montreal, PQ, 1993) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 439, Kluwer Acad. Publ., Dordrecht, 1994, pp. 89–129. MR 1332960
T. W. Gamelin, Uniform Algebras, 2nd ed., Chelsea, New York, 1984.
John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
Georg Pick, Über die Beschränkungen analytischer Funktionen, welche durch vorgegebene Funktionswerte bewirkt werden, Math. Ann. 77 (1915), no. 1, 7–23 (German). MR 1511844, DOI 10.1007/BF01456817
Walter Rudin, Boundary values of continuous analytic functions, Proc. Amer. Math. Soc. 7 (1956), 808–811. MR 81948, DOI 10.1090/S0002-9939-1956-0081948-0
J. Wermer, Pick interpolation for a uniform algebra, Functional analysis and operator theory (Warsaw, 1992) Banach Center Publ., vol. 30, Polish Acad. Sci. Inst. Math., Warsaw, 1994, pp. 333–335. MR 1285619