caa a22 4500 386385424 CHVBK 20180307112056.0 cr unu---uuuuu 161130e198907 xx s 000 0 eng 10.1017/S0305004100068043 doi S0305004100068043 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100068043 Gabardo Jean-Pierre Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada Tempered distributions with spectral gaps [Elektronische Daten] [Jean-Pierre Gabardo] A tempered distribution on whose Fourier transform is supported in an interval [−Ω,Ω], where Ω>0, can be characterized by the behaviour of its successive derivatives. On the other hand, a tempered distribution on whose Fourier transform vanishes in an interval (−Ω,Ω), where Ω>0, can be characterized by the behaviour of a particular sequence of successive antiderivatives. Similar considerations apply to general convolution operators acting on J′(n) and yield characterizations for tempered distributions having their Fourier transforms supported in sets of the form or , where and Ω>0. Copyright © Cambridge Philosophical Society 1989 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/1(1989-07), 143-162 0305-0041 106:1<143 1989 106 PSP https://doi.org/10.1017/S0305004100068043 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100068043 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Gabardo Jean-Pierre Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/1(1989-07), 143-162 0305-0041 106:1<143 1989 106 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge