Abstract
The notions of φ-polynomial expansion % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG% qbciaa-DgacaGGOaWexLMBb50ujbqeguuDJXwAKbacgiGae4hEaGNa% ey4kaSsefCuzVj3zPfgaiCGacaqF5bGaaiykaiabg2da9iaa-Dgaca% GGOaGae4hEaGNaaiykaiabgUcaRiaa-DgacaGGOaGaa0xEaiaacMca% cqGHRaWkdaaeqbqaaiaadchadaWgaaWcbaGaamOBaaqabaGccaGGOa% Gaeqy1dOMaaiikaiab+Hha4jaacMcacaGGPaWaaSaaaeaacaqF5bWa% aWbaaSqabeaacaqFUbaaaaGcbaGaamOBaiaacgcaaaGaey4kaSIaam% OCaiaacIcacqGF4baEcqGFSaalcaqF5bGaaiykaiaacYcaaSqaaiaa% d6gatuuDJXwAK1uy0HMmaeXbfv3ySLgzG0uy0HgiuD3BaGacciab8v% MifkaaigdaaeqaniabggHiLdaaaa!7116!\[g(x + y) = g(x) + g(y) + \sum\limits_{n \geqslant 1} {p_n (\varphi (x))\frac{{y^n }}{{n!}} + r(x,y),} \] and multiplicative addition theorems % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% aaaeaacaaIXaaabaGaamyAaaaadaWcaaqaaiabgkGi2cqaaiabgkGi% 2kaadshaaaqeduuDJXwAKbYu51MyVXgaiuaacqWFvpGAcaWG0bGaey% ypa0JaamisamaaBaaaleaacaGGOaaabeaakmaaBaaaleaacaGGPaaa% beaakiab-v9aQjaadshaaaa!4A8D!\[ - \frac{1}{i}\frac{\partial }{{\partial t}}\varphi t = H_( _) \varphi t\] are introduced and characterization of some φ-polynomial expansions and multiplicative addition theorems are obtained.
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Sponsored by the International Science Foundation (Soros) Grant M3Z00 and by Russian Foundation of Fundamental Research 94-01-0144.
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Buchstaber, V., Kholodov, A. Characteristic expansions and multiplicative addition theorems. Acta Appl Math 43, 233–266 (1996). https://doi.org/10.1007/BF00047925
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DOI: https://doi.org/10.1007/BF00047925