Fq-Linear Calculus over Function Fields
Kochubei, Anatoly N.
Original · EN
We define analogues of higher derivatives for Fq-linear functions over the field of formal Laurent series with coefficients in Fq. This results in a formula for Taylor coefficients of a Fq-linear holomorphic function, a definition of classes of Fq-linear smooth functions which are characterized in terms of coefficients of their Fourier-Carlitz expansions. A Volkenborn-type integration theory for Fq-linear functions is developed; in particular, an integral representation of the Carlitz logarithm is obtained.
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