Abstract
схОДИМОсть ВL p-НОРМЕ Р ьДОВ НА кОМпАктНых ВпОлНЕ НЕсВьжНых гРУппАх г. гАт И Р. тОлЕДО хОРОшО ИжВЕстНО, ЧтО Ч АстНыЕ сУММы РьДОВ ФУРьЕ-ВИлЕНкИНА Дль к АжДОИ ФУНкцИИf ∃L p, 1<p<∞, схОДь тсь кf пО НОРМЕ. Дль лУ БОгО 1≤p≤∞ ОпЕРАтОРы\(S_{M_n } \) тАкжЕ схО Дьтсь пО НОРМЕ кf Дль к АжДОИf ∃L p.
В НАстОьЩЕИ РАБОтЕ Мы ИжУЧАЕМ пОДОБНыЕ сВО ИстВА НА ВпОлНЕ НЕсВьжНых гРУппАх, НЕ ОБьжАтЕль Ных АБЕлЕВых, И Дль сИс тЕМ, сОстОьЩИх Иж пРОИжВЕ ДЕНИИ НОРМИРОВАННых кООРД ИНАтНых ФУНкцИИ Дль Н ЕпРЕРыВНых НЕпРИВОДИМых УНИтАР Ных пРЕДстАВлЕНИИ кООРД ИНАтНых гРУпп. НАкОНЕ ц, Мы УстАНОВлИВАЕМ схОДИ МОсть Дль 1≤p≤∞ сРЕДНИх ФЕИЕ РА В слУЧАЕ ОгРАНИЧЕН Ных гРУпп.
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Research supported by the Hungarian National Foundation for Scientific Research, Grant # F007347; and by the “Alapítvány a Magyar FelsŐoktatásért és Kutatásért”, which is the foundation of the Hungarian Credit Bank, Grant # 485/94.
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Gát, G., Toledo, R. L p-norm convergence of series in compact, totally disconnected groups. Analysis Mathematica 22, 13–24 (1996). https://doi.org/10.1007/BF02342335
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DOI: https://doi.org/10.1007/BF02342335