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where h Ko=2(1 + rh) The modern treatment of the series (1) is due to Fejes [1]. We shall call (1) the F.A. series of f(x) if equations (2) and (3) are satisfied. In this note we are concerned with uniqueness theorems for convergent or summable series of the type (1). An important difference Received by the editors March 1, 1954. ' This note is a simplified account of part of a thesis which was awarded the Ph.D. degree at Queen's University, Belfast, in 1953. 971

Uniqueness theorems for a class of generalized trigonometrical series