Norm preserving extensionsof bounded holomorphic functions

Bounded Holomorphic Functions on Bounded Symmetric Domains

Let D be a bounded homogeneous domain in C , and let A denote the open unit disk. If z e D and /: D —► A is holomorphic, then ß/(z) is defined as the maximum ratio \Vz(f)x\/Hz(x, 3c)1/2 , where x is a nonzero vector in C and Hz is the Bergman metric on D . The number ßf(z) represents the maximum dilation of / at z . The set consisting of all ß/(z), for z e D and /: D —► A holomorphic, is known ...

Norm preserving extensions of holomorphic functions from subvarieties of the bidisk

Weak Topologies on the Bounded Holomorphic Functions

Let G be a region in the complex plane such that there is a nonconstant bounded holomorphic function on G, and denote the algebra of all such functions by BH{G). Let H^{G) denote the Banach algebra that arises when BH{G) is endowed with the supremum norm. In the case where G is the unit disc D, H*>(G) has been extensively studied, mostly by a real-variables analysis of the radial boundary value...

Norm and Numerical Peak Holomorphic Functions on Banach Spaces

We introduce the notion of numerical (strong) peak function and investigate the denseness of the norm and numerical peak functions on complex Banach spaces. Let Ab(BX : X) be the Banach space of all bounded continuous functions f on the unit ball BX of a Banach space X and their restrictions f |B◦ X to the open unit ball are holomorphic. In finite dimensional spaces, we show that the intersecti...

Error Preserving Correction for CPD and Bounded-Norm CPD

In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some difficult scenarios, e.g., when the rank exceeds the tensor dimension, or when the loading components are highly collinear in several or all modes, or when CPD does not have an optimal solution. In such the cases, norms of some rank-1 terms become significantly large, and cancel each other. This makes algorithms getting ...