The Helgason Fourier transform for homogeneous vector bundles over compact Riemannian symmetric spaces—the local theory

The Helgason Fourier transform on noncompact Riemannian symmetric spaces G/K is generalized to the homogeneous vector bundles over the compact dual spaces U/K. The scalar theory on U/K was considered by Sherman (the local theory for U/K of arbitrary rank, and the global theory for U/K of rank one). In this paper we extend the local theory of Sherman to arbitrary homogeneous vector bundles on U/K. For U/K of rank one we also obtain a generalization of the Cartan-Helgason theorem valid for any K-type.     

A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.     

Nuclear structure functions in carbon nearx=1

Data from deep inelastic scattering of 200 GeV muons on a carbon target with squared four-momentum transfer 52 GeV²Q ²200 GeV² were analysed in the region of the Bjorken variable close tox=1, which is the kinematic limit for scattering on a free nucleon. At this value ofx, the carbon structure function is found to beF ₂ ^C 1.2·10^–4. Thex dependence of the structure function forx>0.8 is well described by an exponentialF ₂ ^C exp(–sx) withs=16.5±0.6.Deceased