On the fourier coefficients of functions concentrated on a subset of the circle

Bogomolnaia, A. (1995) On the fourier coefficients of functions concentrated on a subset of the circle. Journal of Mathematical Sciences, 73(6), pp. 633-637. (doi: 10.1007/BF02364941)

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Abstract

We consider T={z∈C:|z|=1},E⊂T ,mE > 0,G(E) is a certain subspace of L 1 (E) consisting of functions concentrated on E and integrable, and {dk}, (k ∈ ℤ) in a summable sequence of positive numbers. It is proved that if G(E)=Lp(E), p≥2, then there exists f∈G(E) such that |f(n)|≥dn, fˆ(n)|⩾dn,n∈Z (one of the questions involved in the majorization problem). Sufficient conditions are obtained for certain other function classes G(E). We study the question of partial majorization. Bibliography: 2 titles.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bogomolnaia, Professor Anna
Authors: Bogomolnaia, A.
College/School:College of Social Sciences > Adam Smith Business School > Economics
Journal Name:Journal of Mathematical Sciences
ISSN:1072-3374
ISSN (Online):1573-8795

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