Results 91 to 100 of about 210 (150)

Finely holomorphic functions and quasi-analytic classes [PDF]

Potential Analysis, 1994
Let \(C\{M_n\}\) be the class of all complex functions \(f: \mathbb{R}\to \mathbb{C}\), \(f\in C^\infty\), which satisfy the inequalities \(|f^{(n)} (x)|< \beta_f B_f M_n\) \((n=0,1, 2,\dots)\), where \(f^{(0)} =f\) and \(\beta_f\), \(B_f\) are constants depending on \(f\), while the constants \(M_n\) satisfy the following inequalities: \(M_0 =1\), \(M^
Pavel Pyrih
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Analytic Properties of Holomorphic Functions

, 1991
At the end of Chapter 1 we introduced the holomorphic functions, that is, those functions f ∈ C1(Ω) that satisfy the Cauchy-Riemann differential equation \(\frac{{\partial f}}{{\partial \bar z}} = 0\) throughout an open set Ω ⊆ ℂ. As an immediate consequence of the topological tools developed in that chapter we found that the holomorphic functions ...
Carlos A. Berenstein, Roger Gay
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VECTOR-VALUED HOLOMORPHIC FUNCTIONS ON THE COMPLEX BALL AND THE ANALYTIC RADON-NIKODYM PROPERTY

Acta Mathematica Scientia, 2000
Summary: The complex Banach spaces \(X\) with values in which every bounded holomorphic function in the unit ball \(B\) of \(\mathbb{C}^d\) \((d> 1)\) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodým property. The proof is based on inner Hardy martingales introduced here.
Zeqian Chen, Caiheng Ouyang
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EXPANSIONS IN SERIES AND THE RATE OF RATIONAL APPROXIMATIONS FOR HOLOMORPHIC FUNCTIONS WITH ANALYTIC SINGULARITIES

Mathematics of the USSR-Sbornik, 1974
It is proved that for functions holomorphic in the complement of an analytic subset of Cn the best rational approximation converges faster than any geometric progression. Bibliography: 3 items.
E M Čirka
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Sufficient conditions for separation of analytic singularities in Cn and a basis for a space of holomorphic functions

Mathematical Notes of the Academy of Sciences of the USSR, 1972
It is proved that every holomorphic function of n variables which has singularities on analytic surfaces, whose equations are linearly dependent, can be represented as the sum of functions, each of which has less than one singular surface. This fact is used to construct a basis for the space of functions which are holomorphic in the domain $$C^n ...
A. P. Yuzhakov
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Holomorphic Spaces Related to Orthogonal Polynomials and Analytic Continuation of Functions

, 2001
We prove three analytic continuation criteria for functions defined on the whole real line, positive half-line and a finite interval. The extended functions belong to certain reproducing kernel holomorphic spaces. The distinctive feature of our theorems is that no smoothness properties of functions to be extended are assumed in the hypotheses ...
Dmitrii Karp
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C k , Weakly Holomorphic Functions on Analytic Sets

Proceedings of the American Mathematical Society, 1973
Joseph Becker
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