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1

Approximation of entire transcendental functions of several complex variables in some Banach spaces for slow growth

Kumar D.

Journal of Applied Analysis

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2017

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Vol. 23, nr 1

9--20

EN

In the present paper, the coefficients characterizations of generalized type Tm(f; α, α) of entire transcendental functions f of several complex variables m (m ≥ 2) for slow growth have been obtained in terms of the sequence of best polynomial approximations of f in the Hardy Banach spaces Hq(Um) and in the Banach spaces Bm(p, q, λ). The presented work is the extension and refinement of the corresponding assertions made by Vakarchuk and Zhir [20-25], Gol’dberg [4] and Sheremeta [17, 18] to the multidimensional case.

2

Several complex variables in Poland

Wiegerinck J.

Wiadomości Matematyczne

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2012

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T. 48, Nr 2

285--292

3

Extended results of the Hadamard product of simple sets of polynomials in hypersphere

El-Sayed A.A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2006

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Vol. 46, [Z] 2

201-213

EN

In this paper we study some extended results of the Hadamard product set for several simple monic sets of polynomials of several complex variables in hyperspherical regions, then we obtain the effectiveness conditions for this Hadamard product in hyperspherical regions.

4

Hoelder continuity property of composite Julia sets

Kosek M.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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Vol. 46, no 4

391-399

EN

In this paper we consider the composite Julia associated with a finite family of the proper polynomial mappings in [C^n]. We show its pluricomplex Green function is Hoelder continous. This yields in particular that the set preserves Markov's inequality.

5

Borne d'invariant metrique pour une famille noetherienne

El Khadiri A.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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Vol. 46, no 3

265-275

EN

The motivation of this paper is a question asked by B. Teissier in [1]: if [fi] : M --> N is an analytic morphism between two real analytic manifolds M and N, and if K is a compact subanalytic set of M, then for every point x[sub 0] in [fi](K) there exists an open neighbourhood U of x[sub 0] in N and a constant [gamma] > 0 such that for all x in U and all (a, b) in the same connected component of [fi^-1(x) intersection of sets K], there exist a rectifiable curve in [fi-1(x) intersection of sets K joining a and b with length less than [gamma]. In this paper we prove the following statement: let [Omega] be an open set of [R^n], N a real analytic manifold, [fi] : [Omega] --> N a proper analytic morphism and [K is a subset of set Omega] an analytic subset of [Omega]. Then for every point y[sub 0] of N there an open neighbourhood U in N and a constant [eta] > 0 such that for all y in U there exists C[sub y] > 0 satisfying the following: for every points a, b of the same connected component of [fi^-1(y) intersection of sets K] there exists an analytic rectifiable curve [sigma] in [fi^-1(y) intersection of sets] K joining a and b with [absolute value of sigma is less than or equal to] C[sub y] [absolute value a - b^eta], where [absolute value of sigma] is the length of [sigma] and [absolute value a - b] is the euclidean distance between a and b.