Summirovanie Funktsional'nykh Ryadov P-Adicheskogo Argumenta

Kniga posvyashchena izucheniyu skhodimosti ryadov Fur'e funktsiy skalyarnogo i vektornogo p-adicheskogo argumenta, prinimayushchikh znacheniya kak v pole obychnykh kompleksnykh chisel, tak i v pole p-adicheskikh kompleksnykh chisel. Pri issledovanii ispol'zuyutsya klassicheskie metody garmonicheskogo i nearkhimedovogo analiza. Dokazannye utverzhdeniya obobshchayut i dopolnyayut rezul'taty, poluchennye ranee v etom napravlenii drugimi avtorami. V knige privedeny issledovaniya skhodimosti ryadov Fur'e kompleksnoznachnykh nepreryvnykh i summiruemykh funktsiy vektornogo r-adicheskogo argumenta, dokazatel'stvo kriteriya m-kratnoy nepreryvnoy differentsiruemosti v terminakh koeffitsientov Malera i dostatochnogo usloviya ravnomernoy skhodimosti ryada Fur'e differentsiruemykh funktsiy p-adicheskogo vektornogo argumenta so znacheniyami v pole kompleksnykh r-adicheskikh chisel, a takzhe issledovanie analiticheskikh svoystv preobrazovaniya Laplasa na prostranstve nepreryvno-differentsiruemykh funktsiy.