Line measures and modular distributions

  • André Unterberger
Part of the Pseudo-Differential Operators book series (PDO, volume 13)


Typically, operators with symbols of arithmetic interest, while acting from \({\mathcal{S}}(\mathbb{R})\) to \({\mathcal{S}^{\prime}}(\mathbb{R})\), have quite bad regularity properties. For instance, even before letting \({N} \nearrow {\infty}\), the ones considered in Chapter 4 could only act on continuous functions, yielding discrete measures as a result. Though building algebras of such operators would be of great interest in several questions, it is impossible to make sense, in general, of the composition of two such operators. In this chapter, we shall describe a way to turn around this difficulty, which has been successful in some instances.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • André Unterberger
    • 1
  1. 1.Department of MathematicsUniversity of ReimsReimsFrance

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