Vol. 95, No. 1, 1981

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Entire functions of exponential type as multipliers for weight functions

Paul Jacob Koosis

Vol. 95 (1981), No. 1, 105–123
Abstract

If W(x) 1 is defined on the real line and satisfies (1), a discussion is given of the regularity assumptions which must be imposed on W in order to guarantee the existence of nonzero entire functions φ of arbitrarily small exponential type making W(x)φ(x) bounded on the real axis. It is known that such φ exist provided that log W(x) is uniformly Lip 1. An example is given which shows, among other things, that this is no longer the case if we merely suppose that log log W(x) is uniformly Lip 1.

Mathematical Subject Classification 2000
Primary: 30D50
Secondary: 42A45
Milestones
Received: 10 March 1980
Published: 1 July 1981
Authors
Paul Jacob Koosis