caa a22 4500 386360413 CHVBK 20180307111913.0 cr unu---uuuuu 161130e198912 xx s 000 0 eng 10.1017/S0004972700017494 doi S0004972700017494 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700017494 On the inversion of Fourier transforms [Elektronische Daten] Let G be a locally compact abelian group, with character group Ĝ. Let ψ be an arbitrary continuous real-valued homomorphism defined on Ĝ. For f in LP(G), 1 < p ≤ 2, let where 1[−ν, ν] is the indicator function of the interval [ − ν, ν ], and I is an unbounded increasing sequence of positive real numbers. Then there is a constant Mp, independent of f, such that M#fp ≤ Mp fp. Consequently, the pointwise limit of the function exists, almost everywhere on G, as ν tends to infinity. Using this result and a generalised version of Riesz's theorem on conjugate functions, we obtain a pointwise inversion for Fourier transforms of functions on Ra × Tb, where a and b are nonnegative integers, and on various other locally compact abelian groups. Copyright © Australian Mathematical Society 1989 Asmar Nakhlé H. Department of Mathematics University of Missouri, Columbia Columbia, MO 65211 United States of America Merryfield Kent G. Department of Mathematics California State University, Long Beach Long Beach, CA 90840 United States of America Bulletin of the Australian Mathematical Society Cambridge University Press 40/3(1989-12), 429-439 0004-9727 40:3<429 1989 40 BAZ https://doi.org/10.1017/S0004972700017494 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700017494 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Asmar Nakhlé H. Department of Mathematics University of Missouri, Columbia Columbia, MO 65211 United States of America NATIONALLICENCE 700 1- Merryfield Kent G. Department of Mathematics California State University, Long Beach Long Beach, CA 90840 United States of America NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 40/3(1989-12), 429-439 0004-9727 40:3<429 1989 40 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge