ON THE LIMITING PROFILE ARISING FROM ORTHONORMALIZING SHIFTS OF EXPONENTIALLY DECAYING FUNCTIONS

It is shown that, under certain conditions, orthonormalizing the posit ive integer shifts of an exponentially decaying function on the half l ine by the Gram-Schmidt process leads to a limiting profile given by o rthonormalizing all their integer shifts on the whole line. These resu lts derive from properties of Cholesky factorization of bi-infinite an d semi-infinite matrices. An example is provided by the negative expon ential function and conjectures are given, supported by numerical evid ence, for the Gaussian and Lorentz function.