Editing Time-scale calculus (section)

==Distributions on time scales==

The [[Dirac delta]] and [[Kronecker delta]] are unified on time scales as the ''Hilger delta'':<ref>{{cite journal |first1=John M. |last1=Davis |first2=Ian A. |last2=Gravagne |first3=Billy J. |last3=Jackson |first4=Robert J. II |last4=Marks |first5=Alice A. |last5=Ramos |title=The Laplace transform on time scales revisited |journal=J. Math. Anal. Appl. |volume=332 |year=2007 |issue=2 |pages=1291–1307 |doi=10.1016/j.jmaa.2006.10.089 |bibcode=2007JMAA..332.1291D |doi-access=free }}</ref><ref>{{cite journal |first1=John M. |last1=Davis |first2=Ian A. |last2=Gravagne |first3=Robert J. II |last3=Marks |title=Bilateral Laplace Transforms on Time Scales: Convergence, Convolution, and the Characterization of Stationary Stochastic Time Series |journal=Circuits, Systems and Signal Processing |year=2010 |volume=29 |issue=6 |pages=1141–1165 |doi=10.1007/s00034-010-9196-2 |s2cid=16404013 }}</ref>

: <math>\delta_{a}^{\mathbb{H}}(t) = \begin{cases}
\dfrac{1}{\mu(a)}, & t = a \\
0, & t \neq a
\end{cases}</math>