Each homotopically homogeneous tube in has an affine-homogeneous base.
Let be a psh function on a bounded pseudoconvex open set , and let be the associated multiplier ideal sheaves, . Motivated by global geometric issues, we establish an effective version of the coherence property of as . Namely, given any , we estimate the asymptotic growth rate in of the number of generators of over , as well as the growth of the coefficients of sections in with respect to finitely many generators globally defined on . Our approach relies on proving asymptotic integral...
It is shown how to embed the polydisk algebras (finite and infinite ones) into the disk algebra A(𝔻̅). As a consequence, one obtains uniform closed subalgebras of A(𝔻̅) which have arbitrarily prescribed stable ranks.
Let be a complex one-dimensional torus. We prove that all subsets of with finitely many boundary components (none of them being points) embed properly into . We also show that the algebras of analytic functions on certain countably connected subsets of closed Riemann surfaces are doubly generated.