Abstract
In this chapter we study the Cauchy problem for parabolic type pseudodifferential equations over the rings of finite adeles and adeles involving a generalization of the Taibleson operator [5, 98]. For the sake of simplicity we formulated all our results for finite adeles and adeles on \(\mathbb{Q}\), however all the results are still valid if the field of rational numbers \(\mathbb{Q}\) is replaced by a global field, i.e. by an algebraic number field, or by the function field of an algebraic curve over a finite field. The results presented in this chapter were obtained by Torba and Zuniga-Galindo in [106].
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