Zur mathematischen Theorie der Druckverbreiterung von Spektrallinien. II

Abstract

This paper continues the discussion of the line profile on the wings. It differs from [2] mainly insofar as it is now not assumed that skalar additivity of the single perturbations yields. Anderson's formula ceases to be valid and no analogous closed formula seems to exist. Nevertheless, the discussion is possible and yields the result predicted in [2]. Chapter I considers the convolution of tight measures on topological Abelian semi-groups. Chapter II treats Poisson measures, a new concept for the statistical model of an infinite gas in [2]. To every positive Radon measure ρ on a locally compact set $$\mathfrak{X}$$ one associates a positive measure P(ρ) on the space of all positive Radon measures on $$\mathfrak{X}$$ with the vague topology. The map ρ→P(ρ) is continuous in various ways and has the property P(ρ + σ) = P(ρ)*P(σ), P(0) = $$\mathfrak{d}$$ 0 (Dirac measure at the measure 0). In III and IV the discussion of the line profile is carried out. The most important tool is a homogeneity relation established at the beginning of IV.