Unilateral Laplace Transforms on Time Scales

Convergence of Unilateral Laplace Transforms on Time Scales

A time scale is any closed subset of the real line. Continuous time and discrete time are special cases. The unilateral Laplace transform of a signal on a time scale subsumes the continuous-time unilateral Laplace transform, and the discretetime unilateral z-transform as special cases. The regions of convergence (ROCs) time scale Laplace transforms are determined by the time scale’s graininess....

Bilateral Laplace Transforms on Time Scales: Convergence, Convolution, and the Characterization of Stationary Stochastic Time Series

The convergence of Laplace transforms on time scales is generalized to the bilateral case. The bilateral Laplace transform of a signal on a time scale subsumes the continuous time bilateral Laplace transform, and the discrete time bilateral z-transform as special cases. As in the unilateral case, the regions of convergence (ROCs) time scale Laplace transforms are determined by the time scale’s ...

The Laplace transform on isolated time scales

Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is considered in more detail by proving the convolution theorem and a discrete analogue of the classica...

The Laplace transform on time scales revisited ✩

In this work, we reexamine the time scale Laplace transform as defined by Bohner and Peterson [M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001; M. Bohner, A. Peterson, Laplace transform and Z-transform: Unification and extension, Methods Appl. Anal. 9 (1) (2002) 155–162]. In particular, we give conditions on the class of func...

A note on the comparison between Laplace and Sumudu transforms