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53,974
Free holomorphic functions and interpolation
 Math. Ann
"... Abstract. In this paper we obtain a noncommutative multivariable analogue of the classical NevanlinnaPick interpolation problem for analytic functions with positive real parts on the open unit disc. Given a function f: Λ → C, where Λ is an arbitrary subset of the open unit ball Bn: = {z ∈ C n: ‖z ‖ ..."
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Cited by 15 (3 self)
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‖ < 1}, we find necessary and sufficient conditions for the existence of a free holomorphic function g with complex coefficients on the noncommutative open unit ball [B(H) n]1 such that Re g ≥ 0 and g(z) = f(z), z ∈ Λ, where B(H) is the algebra of all bounded linear operators on a Hilbert space H
SEMIGROUPS OF HOLOMORPHIC FUNCTIONS IN THE POLYDISK
"... (Communicated by Franc Forstneric) Abstract. In this paper we provide an easytouse characterization of infinitesimal generators of semigroups of holomorphic functions in the polydisk. We also present a number of examples related to that characterization. ..."
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(Communicated by Franc Forstneric) Abstract. In this paper we provide an easytouse characterization of infinitesimal generators of semigroups of holomorphic functions in the polydisk. We also present a number of examples related to that characterization.
QUASICONFORMAL DEFORMATIONS OF HOLOMORPHIC FUNCTIONS
"... on the occasion of his 110th birthday Abstract. This paper deals with holomorphic functions from Bergman spaces Bp in the disk and provides the existence of deformations (variations) which do not increase the norm of functions and preserve some other prescribed properties. Admissible variations are ..."
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on the occasion of his 110th birthday Abstract. This paper deals with holomorphic functions from Bergman spaces Bp in the disk and provides the existence of deformations (variations) which do not increase the norm of functions and preserve some other prescribed properties. Admissible variations
Leafwise holomorphic functions
 Proc. of the AMS
, 2003
"... It is a wellknown and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property holds in the setting of holomorphically foliated spaces. 1 In ..."
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Cited by 5 (4 self)
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It is a wellknown and elementary fact that a holomorphic function on a compact complex manifold without boundary is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property holds in the setting of holomorphically foliated spaces. 1
Extension Problem of Holomorphic Functions
"... In the Summer Seminar at Tateyama on Several Complex Variables, 18th July 1994, Professor T. $\mathrm{O}\mathrm{h}\mathrm{s}\mathrm{a}\mathrm{w}\mathrm{a}[19] $ posed the following problem. Let $\Omega $ be a bounded pseudoconvex domain in $\mathrm{C}^{n} $ and $H $ be a onecodimensional complex li ..."
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linear subspace of $\mathrm{C}^{n} $. For any bounded holomorphic function $g $ on $\Omega\cap H $ , does there exist a bounded holomorphic function $f $ on $\Omega $ such that the restriction $f\Omega\cap H $ of $f $ to $\Omega\cap H $ coincides with $g $ on $\Omega\cap H$? We give a counterexample
On Limits of Sequences of Holomorphic Functions
"... Abstract: We study functions which are the pointwise limit of a sequence of holomorphic functions. In one complex variable this is a classical topic, though we offer some new points of view and new results. Some novel results for solutions of elliptic equations will be treated. In several complex va ..."
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Cited by 2 (0 self)
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Abstract: We study functions which are the pointwise limit of a sequence of holomorphic functions. In one complex variable this is a classical topic, though we offer some new points of view and new results. Some novel results for solutions of elliptic equations will be treated. In several complex
ON THE ORDER OF HOLOMORPHIC AND CHOLOMORPHIC FUNCTIONS
, 2007
"... Abstract. In the first part of this paper we prove that the Lojasiewicz exponent of a nonconstant holomorphic germ f: (Cm, 0) → (C, 0) is a good exponent for f coinciding with the order of vanishing of f at zero and the degree at zero of its cycle of zeroes Zf. As an application of this result we ..."
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Cited by 1 (1 self)
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we show that for any holomorphic curve germ γ: (C, 0) → (Cm, 0) one has ord0(f ◦ γ) = ord0f · ord0γ if and only if γ is transversal to f−1(0) at zero. In a recent paper we have introduced an order of flatness for cholomorphic functions which allowed us to give some bounds on the Lojasiewicz ex
SEPARATING SINGULARITIES OF HOLOMORPHIC FUNCTIONS
"... ABSTRACT. We present a short proof for a classical result on separating singularities of holomorphic functions. The proof is based on the open mapping theorem and the fusion lemma of Roth, which is a basic tool in complex approximation theory. The same method yields similar separation results for ot ..."
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Cited by 1 (0 self)
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ABSTRACT. We present a short proof for a classical result on separating singularities of holomorphic functions. The proof is based on the open mapping theorem and the fusion lemma of Roth, which is a basic tool in complex approximation theory. The same method yields similar separation results
Relative solidity for spaces of holomorphic functions
"... We dene and investigate relative solidity for sequence spaces, and use it to study spaces of holomorphic functions on the unit disk and related coecient multiplier spaces. ..."
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Cited by 3 (0 self)
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We dene and investigate relative solidity for sequence spaces, and use it to study spaces of holomorphic functions on the unit disk and related coecient multiplier spaces.
Topologies on the Space of Holomorphic Functions
, 707
"... We remark that the result presented here can be proved more simply using the closed graph theorem. However we believe that our results can be used to prove a more interesting result. Details to follow in a later paper. ..."
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We remark that the result presented here can be proved more simply using the closed graph theorem. However we believe that our results can be used to prove a more interesting result. Details to follow in a later paper.
Results 1  10
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53,974