Rational approximation on product sets

Author:
Otto B. Bekken

Journal:
Trans. Amer. Math. Soc. **191** (1974), 301-316

MSC:
Primary 32E30; Secondary 46J10

MathSciNet review:
0379900

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Abstract: Our object here is to study pointwise bounded limits, decomposition of orthogonal measures and distance estimates for where and are compact sets in the complex plane.

**[1]**O. B. Bekken,*Products of algebras on plane sets*, U.C.L.A. Thesis, 1972.**[2]**Andrew Browder,*Point derivations on function algebras*, J. Functional Analysis**1**(1967), 22–27. MR**0211262****[3]**Brian Cole and R. Michael Range,*𝐴-measures on complex manifolds and some applications*, J. Functional Analysis**11**(1972), 393–400. MR**0340646****[4]**A. M. Davie,*Bounded limits of analytic functions*, Proc. Amer. Math. Soc.**32**(1972), 127–133. MR**0293069**, 10.1090/S0002-9939-1972-0293069-1**[5]**A. M. Davie, T. W. Gamelin, and J. Garnett,*Distance estimates and pointwise bounded density*, Trans. Amer. Math. Soc.**175**(1973), 37–68. MR**0313514**, 10.1090/S0002-9947-1973-0313514-8**[6]**Theodore W. Gamelin,*Uniform algebras*, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. MR**0410387****[7]**T. W. Gamelin and J. Garnett,*Constructive techniques in rational approximation*, Trans. Amer. Math. Soc.**143**(1969), 187–200. MR**0249639**, 10.1090/S0002-9947-1969-0249639-4**[8]**-,*Bounded approximation by rational functions*(to appear).**[9]**G. M. Henkin,*Integral representation of functions which are holomorphic in strictly pseudoconvex regions, and some applications*, Mat. Sb. (N.S.)**78 (120)**(1969), 611–632 (Russian). MR**0249660****[10]**Donald Sarason,*Generalized interpolation in 𝐻^{∞}*, Trans. Amer. Math. Soc.**127**(1967), 179–203. MR**0208383**, 10.1090/S0002-9947-1967-0208383-8

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1974-0379900-6

Keywords:
Pointwise bounded approximation,
rational functions,
orthogonal measures,
Vitushkin techniques,
weak-star closure in

Article copyright:
© Copyright 1974
American Mathematical Society