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.