Linear Differential Elimination for Analytic Functions

This paper provides methods to decide whether a given analytic function of several complex variables is a linear combination of finitely many given analytic functions with coefficients of the following special form: Each one of these coefficients is a composition of an unknown analytic function of less arguments than the function to be expressed, with fixed analytic functions. Methods which compute suitable coefficient functions in the affirmative case are presented as well.     

Some Local Contour-Solid Theorems for Finely Holomorphic Functions

We prove some local contour-solid theorems for finely holomorphic functions defined on sets of the complex plane that are finely open with nonpolar complements.     

Third-Order Differential Subordinations for Analytic Functions Associated with Generalized Mittag-Leffler Functions

In this paper, third-order differential subordination results are obtained for analytic functions associated with an operator defined by the normalized form of the generalized Mittag-Leffler functions. Some particular cases involving Mittag-Leffler and hyperbolic functions are also considered.     

On Certain Inequalities for Some Analytic Functions and Differential Subordinations

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Analytic Functions with Negative Coefficients and Differential and Integral Operators

In this paper integral properties of some analytic functions with negative coefficients from certain classes of functions defined using Ruscheweyh differential operator are studied. The obtained results are sharp and they are improvement of some known results.     

Equivalence of Differential Operators in Spaces of Analytic Functions over the Tate Field

We obtain conditions for the equivalence of certain differential operators in spaces of analytic functions over the Tate field.     

由广义微分算子定义的某些解析函数类的优化性质

本文首先引入了由广义微分算子定义的某些$p$叶解析函数新子类$S_{p,q,\lambda}^{m,j,l}[A,B;\gamma]$ 和 $H_{p,q,\lambda}^{m,j,l}(\alpha,\beta)$, 然后研究了该子类的优化性质, 所得结果推广了某些已知结论.     

Analytic Extension of Functions from Analytic Hilbert Spaces

Let M be an invariant subspace of Hv2. It is shown that for each f∈M⊥, f can be analytically extended across (?)Bd\σ(Sz1,…, Szd).     

Expansion of Analytic Functions in Series of Floquet Solutions of First Order Differential Systems

In this paper we study boundary eigenvalue problems for first order systems of ordinary differential equations of the form \[zy'\left( z \right) = \left( {\lambda A_1 \left( z \right) + A_0 \left( z \right)} \right)y\left( z \right),\,\,y\left( {ze^{2\pi i} } \right) = e^{2\pi iv} y\left( z \right)\] for z ? S^log, where S is a ring region around zero, S^log denotes the Riemann surface of the logarithm over S, the coefficient matrix functions A₁(z) and A₀(z) are holomorphic on S, and v is a complex number. The eigenfunctions of this eigenvalue problem are the Floquet solutions of the differential system with v as characteristic exponent. For an open subset S₀ of S, the notion of A₁-convexity of the pair (S₀, S) is introduced. For A₁-convex pairs (S₀, S) it is shown that the expansion into eigenfunctions and associated functions of holomorphic functions on S^log, satisfying the monodromy condition y(ze^2πi) = e^2πivy(z), converges regularly on S^log₀ and is unique. If S is a pointed neighbourhood of 0 and A₁(z) is holomorphic in SU{0}, it is shown that there is a pointed neighbourhood S₀ of 0 such that (S₀, S) is A₁-convex. It follows from the results of this paper that many expansions of analytic functions in terms of special functions can be considered as eigenfunction expansions of this kind.     

Linear Generalized Analytic Functions

Complex-valued continuous functions are approximated using solutions of complex partial differential equations of Vekua type.     

Stable Extrapolation of Analytic Functions

Foundations of Computational Mathematics - This paper examines the problem of extrapolation of an analytic function for $$x > 1$$ given $$N+1$$ perturbed samples from an equally spaced grid...     

Analytic Extension of Smooth Functions

Let F be a closed proper subset of ?ⁿ and let ?* be a class of ultradifferentiable functions. We give a new proof for the following result of Schmets and Valdivia on analytic modification of smooth functions: for every function ? ∈ ?* (?ⁿ) there is ${\widetilde f} \in {\cal E}_{*}(\rm R ^{n})$ which is real analytic on ?ⁿF and such that ?^a ? ¦ _F = ?^a ? ¦ _F for any a ∈ ?₀ ⁿ. For bounded ultradifferentiable functions ? we can obtain ${\widetilde f}$ by means of a continuous linear operator.     

Pervasive Algebras of Analytic Functions

We characterize those open U in the sphere such that A(U) is complex-pervasive, and those such that Re A(U) is real-pervasive. Pervasive means, roughly, that the uniform closure on each proper closed subset of bdy U is the space of all continuous functions (to or , as the case may be).     

线性同胚于星象函数的一族解析函数

本文定义了线性同胚于星象函数的－族解析函数Ａ（，α）．我们导出Ａ（α）中函数的积分表达式：借助算子理论研究Ａ（，α）族的包含关系并确定它的闭凸包、闭凸包的极值点和它的支撑点；利用一个阶微分从属证明关于实部的二个不等式．最后，我们还证明Ａ（，α）中函数的偏差定理．     

含有解析函数与亚纯函数的一些不等式

指出文献 [2 ]和文献 [4]中的错误 ,并且得到含有单位圆盘内接解析函数与亚纯函数的几个不等式 .     

解析函数与Lipschitz条件

研究了解析函数与Lipschitz条件,得到了如下两个结果:(i)设D是一平面区域,f(z)在D中解析,00,对任意z∈D有|f′(z)|≤md(z,D)k-1,则f∈Lipk(D)且‖f‖k≤cmk,其中c=c(D)是仅与D有关的常数.     

Inequalities for Majorizing Analytic Functions

For analytic functions satisfyingMeyman's majorization conditions, with the use of classical properties of conformal mappings exact inequalities complementing and strengthening the results of Akhiezer and Meyman are derived. As a corollary, for the modulus of the derivative of a rationally-trigonometric function a Bernstein type bound, which implies the result by Borwein, Erdelyi, and Zhang, is obtained. Bibliography: 10 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 155–173.