In [11], Zhu proved that a

holomorphic function belongs to Bloch space if and only if it is hyperbolic Lipschitz.

[??]([epsilon], z) is the 1-Gevrey asymptotic expansion as e tends to 0 of a

holomorphic function f([epsilon], z) in S([theta], [gamma]; E) x [D.sub.r]; (c) if [gamma] > [pi] is chosen so that (4) holds, then the formal series [??]([epsilon], z) is, by an analogue of Borel-Ritt's theorem for Gevrey asymptotic expansion (see, e.g., Section 3.2 of [2]), 1-summable in the direction d and its sum equals f([epsilon], z).

Moreover the Hamiltonian is a

holomorphic function at a neighborhood of the origin(equilibrium); the linear part of the first-order ordinary form of (35) coincides with

Keywords:

Holomorphic function, subharmonic function, Hausdorff measure, exceptional sets.

Consider the

holomorphic function F(z) := [??](z) - z defined on [B.sub.[delta]].

a rectangle) is conformally mapped onto another regular region, then this mapping is performed by a

holomorphic function. This mapping is fully determined by its values on an arbitrarily small open subset of the region.

where F is a

holomorphic function from R x [R.sup.n] into [R.sup.n], for n [greater than or equal to] 1.

Let f be a

holomorphic function on X such that Sing(X) [subset] A = {f = 0}.

We recall that a Pick function is a

holomorphic function [phi] in the upper half-plane H with [??][phi](z) [greater than or equal to] 0 for z [member of] H Pick functions are extended by reflection to

holomorphic functions in C\R and they have the following integral representation

G(x/t, t) is a

holomorphic function of t in some annulus about t = 0.

The major part of realization theory concerns the identification of a given

holomorphic function as a transfer (characteristic) function of a system (colligation) or a linear fractional transformation of such a function.

We define a

holomorphic function [sub.x3,18] on [[unknown character].sub.3] as