ABSTRACT
In this chapter we present basic preparatory material which is needed for approximate integration over volumes, i.e., regular regions in Euclidean space ℝ q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315195674/823ed023-dd6c-41bb-a456-22174b64a780/content/imath17_1.tif"/> . We start with the introduction of lattices in Section 17.1. Then we are concerned in Section 17.2 with multivariate periodic polynomials. Section 17.3 delivers vector analytic background in the Euclidean space ℝ q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315195674/823ed023-dd6c-41bb-a456-22174b64a780/content/imath17_2.tif"/> . Green’s theorems are recapitulated for regular regions. It follows the representation of the essentials for classical Fourier theory (in Section 17.4) and its weak variants in Gauss–Weierstrass context. The chapter ends with the concept of periodization in its manifestation involving the Poisson summation formula (in Section 17.5).
