Geodesic
Polynomial Hulls of Sets Invariant Under an Action of the Special Unitary Group
Canadian journal of mathematics, Tome 40 (1988) no. 5, pp. 1256-1271

Voir la notice de l'article provenant de la source Cambridge University Press

If K is a compact subset of C n , will denote the polynomial hull of K: arises in the study of uniform algebras as the maximal ideal space of the algebra P(K) of uniform limits on K of polynomials (see [3]). The condition (K is polynomially convex) is a necessary one for uniform approximation on K of continuous functions by polynomials (P(K) = C(K)). If K is not polynomially convex, the question of existence of analytic structure in is of particular interest. For n = 1, is the union of K and the bounded components of C\K. The determination of in dimensions greater than one is a more difficult problem. Among the special classes of compact sets K whose polynomial hulls have been determined are those invariant under certain group actions on C n . 
Anderson, John T. Polynomial Hulls of Sets Invariant Under an Action of the Special Unitary Group. Canadian journal of mathematics, Tome 40 (1988) no. 5, pp. 1256-1271. doi: 10.4153/CJM-1988-054-9
@article{10_4153_CJM_1988_054_9,
     author = {Anderson, John T.},
     title = {Polynomial {Hulls} of {Sets} {Invariant} {Under} an {Action} of the {Special} {Unitary} {Group}},
     journal = {Canadian journal of mathematics},
     pages = {1256--1271},
     year = {1988},
     volume = {40},
     number = {5},
     doi = {10.4153/CJM-1988-054-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-054-9/}
}
TY  - JOUR
AU  - Anderson, John T.
TI  - Polynomial Hulls of Sets Invariant Under an Action of the Special Unitary Group
JO  - Canadian journal of mathematics
PY  - 1988
SP  - 1256
EP  - 1271
VL  - 40
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-054-9/
DO  - 10.4153/CJM-1988-054-9
ID  - 10_4153_CJM_1988_054_9
ER  - 
%0 Journal Article
%A Anderson, John T.
%T Polynomial Hulls of Sets Invariant Under an Action of the Special Unitary Group
%J Canadian journal of mathematics
%D 1988
%P 1256-1271
%V 40
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-054-9/
%R 10.4153/CJM-1988-054-9
%F 10_4153_CJM_1988_054_9

[1] 1. Adams, F., Lectures on Lie groups (W. A. Benjamin, N.Y., 1969). Google Scholar

[2] 2. Bjork, J.-E., Compact groups operating on Banach algebras, Math. Ann. 205 (1973), 281–297. Google Scholar

[3] 3. Browder, A., Introduction to function algebras (W. A. Benjamin, N.Y., 1969). Google Scholar

[4] 4. Browder, A., Cohomology of maximal ideal spaces, Bull. A.M.S. 67 (1961), 515–516. Google Scholar

[5] 5. Debiard, A. and Gaveau, B., Equations de Cauchy-Riemann sur SU(2) et leurs enveloppes d'holomorphie, Can. J. Math. 38 (1986), 1009–1024. Google Scholar

[6] 6. Gamelin, T., Hartogs series, Hartogs functions, and Jensen measures, in Spaces of analyticfunctions, Kristiansand, Norway (1975), Lecture Notes in Mathematics 512 (Springer-Verlag, N.Y., 1976). Google Scholar

[7] 7. Helgason, S., Differential geometry and symmetric spaces (Academic Press, N.Y., 1962). Google Scholar

[8] 8. Helms, L. L., Introduction to potential theory (John Wiley & Sons, N.Y., 1969). Google Scholar

[9] 9. Hormander, L. and J. Wermer, Uniform approximation on compact subsets in n , Math. Scand. 23 (1968), 5–21. Google Scholar

[10] 10. Hua, L. K., On the theory ofautomorphic functions of a matrix variable I, Geometrical basis, Amer. J. Math. 66 (1944), 470–480. Google Scholar

[11] 11. Rudin, W., Function theory on the unit ball in n (Springer-Verlag, N.Y., 1980). Google Scholar | DOI

[12] 12. Wermer, J., Subharmonicity and hulls, Pac. J. Math. 38 (1975), 283–290. Google Scholar

Cité par Sources :