Analysis and Prbability over Infinite Extensions of a Local Field |
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Authors: | Kochubei Anatoly N |
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Institution: | (1) Institute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivska 3, Kiev, 252601, Ukraine. E-mail |
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Abstract: | We consider an infinite extension K of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. K is equipped with an inductive limit topology; its conjugate K; is a completion of K with respect to a topology given by certain explicitly written semi-norms. We construct and study a Gaussian measure, a Fourier transform, a fractional differentiation operator and a cadlag Markov process on K. If we deal with Galois extensions then all these objects are Galois-invariant. |
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Keywords: | local field field extension Gaussian measure Fourier transform stable process fractional differentiation |
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