Hadamard product of certain classes of functions

• Autorzy: Piejko K.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider the Hadamard product * of regular functions using the concept of subordination. Let P(A,B) denote the class of regular functions subordinated to the linear fractional transformation (1 + Az)/(1 - Bz), where A + B ≠ 0 and \B\ ≤ 1. By P(A,B)* P(C,D) we denote the set, {f * g : f ∈ P(A,B), g ∈ P(C,D)}. It is known ([3], [7]). that for some complex numbers A,B,C,D there exist X and Y such that P(A, B) * P(C, D) ⊂ P(X, Y). The purpose of this note is to find the necessary and sufficient conditions for the equality of the classes P(A, B) * P(C, D) and P{X, Y).

Słowa kluczowe

EN

Hadamard product; convolution; subordination; bounded functions

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2005
• Tom: Vol. 11, nr 1
• Strony: 145--151
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Piejko K.

• Department of Mathematics, Rzeszów University of Technology, W. Pola 2, 35-959 Rzeszów, Poland,

Bibliografia

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• [2] Landau, E., Darstellung und Begründung einiger neurer Ergebnise der Funktionentheorie, Chelsea Publishing Co., New York, 1946.
• [3] London, R. R., A convolution theorem for functions mapping the unit disc into half planes, Math. Japon. 43(1) (1996), 23-29.
• [4] Piejko, K., On some convolution theorems, Comment. Math. Prace Mat. 42(1) (2002), 103-112.
• [5] Piejko, K., Sokół, J., Stankiewicz J., On some problem of the convolution of bounded functions, North-Holland Math. Stud. 197 (2004), 229-238.
• [6] Rogosinski, W., On the coefficients of subordinated functions, Proc. London Math. Soc. (2) 48 (1943), 48-82.
• [7] Stankiewicz, J., Stankiewicz, Z., Convolution of some classes of function, Folia Sci. Univ. Tech. Resov. Math. 7 (1988), 93-101.