ABSTRACT
In one-dimensional theory we saw how the Helmholtz operator Δ + λ can be used to formulate quadrature rules adapted to certain oscillation properties of the integrand by a particular choice of the “wave parameter” λ (cf. Chapter 6). In this chapter we extend this approach to the multivariate case. To this end we introduce Λ-lattice functions G(Δ + λ; ·) with respect to the (Helmholtz) operators Δ + λ, λ ∈ ℝ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315195674/823ed023-dd6c-41bb-a456-22174b64a780/content/imath20_1.tif"/> , and the “boundary condition of periodicity”. We restrict our Helmholtz approach only to features which are different to the Laplace context.
