Antisymmetry and analytic structure in the spectrum of a uniform Fréchet algebra
Let M be a \(C^{\infty}\)-smooth submanifold of a domain \(G\subset C^ n\). Denote by 0(M) the algebra of germs of holomorphic functions on M, that is, each \(f\in 0(M)\) is holomorphic in some neighbourhood of M, the neighbourhood dependent of f. Now define A(M) as the closure of 0(M) with respect to the topology of compact convergence on M. If M coincides with \(\sigma\) A(M), the spectrum of A(M), we give a necessary and sufficient condition for A(M) such that M is a complex manifold.
analytic structure in the spectrum of a uniform Fréchet algebra
algebra of germs of holomorphic functions
scientific article; zbMATH DE number 4004941
scientific article