The use of operators for the construction of normal bases for the space of continuous functions on Vq
نویسنده
چکیده
Let a and q be two units of Zp, q not a root of unity, and let Vq be the closure of the set {aqn | n = 0, 1, 2, ..}. K is a non-archimedean valued field, K contains Qp, and K is complete for the valuation |.|, which extends the p-adic valuation. C(Vq → K) is the Banach space of continuous functions from Vq to K, equipped with the supremum norm. Let E and Dq be the operators on C(Vq → K) defined by (Ef)(x) = f(qx) and (Dqf)(x) = (f(qx)− f(x))/(x(q − 1)). We will find all linear and continuous operators that commute with E (resp. with Dq), and we use these operators to find normal bases for C(Vq → K).
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