The Toolkit for Computations

  • Michał EcksteinEmail author
  • Bruno Iochum
Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 27)


In this chapter we introduce a number of mathematical tools, which will prove useful in the spectral action computations. Firstly, we consider the basic properties of some spectral functions via the functional calculus and general Dirichlet series. Next, we study the interplay between these provided by the functional transforms of Mellin and Laplace. The remainder of the chapter is devoted to various notions from the theory of asymptotic behaviour of functions and distributions.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Copernicus Center for Interdisciplinary StudiesKrakówPoland
  2. 2.Faculty of Physics, Astronomy and Applied Computer ScienceJagiellonian UniversityKrakówPoland
  3. 3.National Quantum Information Centre, Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and InformaticsUniversity of GdańskGdańskPoland
  4. 4.Aix-Marseille Univ, Université de Toulon, CNRS, CPTMarseilleFrance

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