Abstract
In this work, it is shown that for the classical Cartan domain mathcal {R}_{II} consisting of symmetric 2times 2 matrices, every algebraic subset of mathcal {R}_{II}, which admits the polynomial extension property, is a holomorphic retract.
Highlights
Denote by RII the classical Cartan domain of type II, i.e. RII = A ∈ M2×2(C) : A = AT, I − A∗A > 0 .Here M2×2(C) stands for the space of 2 × 2 matrices with complex elements and I is the unit matrix.In this paper, we examine certain varieties V of RII for which the restrictions of polynomials to V can be extended to holomorphic functions on RII without increasing their supremum norm
We examine certain varieties V of RII for which the restrictions of polynomials to V can be extended to holomorphic functions on RII without increasing their supremum norm
The origin of that sort of studies goes back to Rudin’s book [13] and one of the goals is to determine whether such a set V is a holomorphic retract
Summary
We say that two points x, y of RII form a balanced pair if there are an automorphism φ and a complex scalar a such that x = φ(0) and y = We can assume that 0 is a regular point of W , which means that W is near 0 a one-dimensional complex submanifold, i.e. it can be written as a graph (λ, g(λ)) of a holomorphic function g such that g(0) = 0, |λ| < .
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