The Michigan Mathematical Journal

Rational approximation on the unit sphere in C2

Article information

Source
Michigan Math. J., Volume 52, Issue 1 (2004), 105-117.

Dates
First available in Project Euclid: 1 April 2004

https://projecteuclid.org/euclid.mmj/1080837737

Digital Object Identifier
doi:10.1307/mmj/1080837737

Mathematical Reviews number (MathSciNet)
MR2043399

Citation

Anderson, John T.; Izzo, Alexander J.; Wermer, John. Rational approximation on the unit sphere in C 2. Michigan Math. J. 52 (2004), no. 1, 105--117. doi:10.1307/mmj/1080837737. https://projecteuclid.org/euclid.mmj/1080837737

References

• H. Alexander and J. Wermer, Several complex variables and Banach algebras, 3rd ed., Springer-Verlag, New York, 1998.
• J. Anderson and J. Cima, Removable singularities for $L^p$ CR functions, Michigan Math. J. 41 (1994), 111--119.
• ------, The Henkin transform and approximation on the unit sphere in $C^2,$ unpublished manuscript.
• J. Anderson and A. Izzo, A peak point theorem for uniform algebras generated by smooth functions on two-manifolds, Bull. London Math. Soc. 33 (2001), 187--195.
• R. F. Basener, On rationally convex hulls, Trans. Amer. Math. Soc. 182 (1973), 353--381.
• H. S. Bear, Complex function algebras, Trans. Amer. Math. Soc. 90 (1959), 383--393.
• A. Browder, Introduction to function algebras, Benjamin, New York, 1969.
• P. L. Duren, Theory of $H^ p$ spaces, Academic Press, New York, 1970.
• T. Gamelin, Uniform algebras, 2nd ed., Chelsea, New York, 1984.
• G. M. Henkin, H. Lewy's equation and analysis on pseudoconvex manifolds, Russian Math. Surveys 32 (1977), 59--130.
• L. Hörmander, An introduction to complex analysis in several variables, North-Holland, Amsterdam, 1973.
• L. Hörmander and J. Wermer, Uniform approximation on compact sets in $\bold C^n,$ Math. Scand. 23 (1968), 5--21.
• A. Izzo, Uniform algebras generated by holomorphic and pluriharmonic functions on strictly pseudoconvex domains, Pacific J. Math. 171 (1995), 429--436.
• H. P. Lee, Orthogonal measures for subsets of the boundary of the ball in $\Bbb C^ 2,$ Ph.D. thesis, Brown University, Providence, RI, 1979.
• H. P. Lee and J. Wermer, Orthogonal measures for subsets of the boundary of the ball in $\bold C^2,$ Recent developments in several complex variables (Princeton, 1979), pp. 277--289, Princeton Univ. Press, Princeton, NJ, 1981.
• J. Merker and E. Porten, On removable singularities for integrable CR functions, Indiana Univ. Math. J. 48 (1999), 805--856.
• W. Rudin, Function theory in the unit ball of $\bold C^n,$ Springer-Verlag, Berlin, 1980.
• E. L. Stout, The theory of uniform algebras, Bogden & Quigley, Tarrytown-on-Hudson, NY, 1971.
• N. Th. Varopoulos, BMO functions and the $\bar\partial$-equation, Pacific J. Math. 71 (1977), 221--273.
• J. Wermer, Polynomially convex disks, Math. Ann. 158 (1965), 6--10.