is known as a (formal) Laplace–Stieltjes integral.
If the integral converges for some complex number , then it converges for all with , and the function is then the Laplace–Stieltjes transform of . If is of the form for a function on that is Lebesgue integrable for all (see Lebesgue integral), then the Laplace–Stieltjes transform becomes the Laplace transform of .
There is also a corresponding two-sided Laplace–Stieltjes transform (or bilateral Laplace–Stieltjes transform) for suitable functions .
See Laplace transform for additional references.
|[a1]||D.V. Widder, "An introduction to transform theory" , Acad. Press (1971)|
Laplace-Stieltjes transform. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Laplace-Stieltjes_transform&oldid=22709