The main purpose of this article is to present a generalization Forelli’s theorem for functions holomorphic along suspension integral curves diagonalizable vector field aligned type. For purpose, we develop new capacity theory that generalizes the projective introduced by Siciak (Sophia Kokyuroku Math 14:1–96, 1982). Our improves results Kim et al. (J Geom Anal 19(3):655–666, 2009) and Cho (Com...

We consider the problem of identifying boundary values of holomorphic functions on (non-smooth) bounded domains in C 2 with boundaries that are Levi-at oo of a small set. Assuming also that the domain is circular, we construct a type of extension operator from the algebra of bounded holomorphic functions on a leaf of the induced Levi-foliation to the algebra of bounded holomorphic functions on ...

Holomorphic almost modular forms are holomorphic functions of the complex upper half plane which can be approximated arbitrarily well (in a suitable sense) by modular forms of congruence subgroups of large index in SL(2,Z). It is proved that such functions have a rotation-invariant limit distribution when the argument approaches the real axis. An example for a holomorphic almost modular form is...

We define a free holomorphic function to be a function that is locally a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an OkaWeil theorem for free analytic functions.