Square integrability of Gaussian bells on time scales

Abstract

We will consider a generalization E(x) of the continuum Gaussian bell e -x2/2 on a time scale I". A crucial question is whether this Gaussian bell is square integrable on the corresponding time scale. We will see that this is not the case in general. We establish sufficient and necessary conditions for the time scale T to satisfy E 6 L2('Y). (~)

Comparison theorems of Hille–Wintner type for dynamic equations on time scales

“…A time scale that is important in the theory of orthogonal polynomials and quantum theory (cf., e.g., [14], [19]…”