an:06073408
Zbl 1252.44001
Chaudhary, M. S.; Tikare, Sanket A.
On gauge Laplace transform
EN
Int. J. Math. Anal., Ruse 5, No. 33-36, 1733-1740 (2011).
00297074
2011
j
44A10 26A39 44A20
Laplace transform; Henstock-Kurzweil integral; inversion formula; Laplace-Stieltjes transform; gauge integrals; gauge Laplace transform
The Laplace transform (Riemann integral) and the Laplace-Stieltjes transform (Lebesgue integral) have been studied by many authors [\textit{I. N. Sneddon}, The use of integral transforms. New York etc.: McGraw-Hill Book Company. (1972; Zbl 0237.44001); \textit{L. Debnath}, Integral transforms and their applications. Boca Raton, FL: CRC Press. (1995; Zbl 0920.44001); \textit{D. V. Widder}, The Laplace transform. New York. Princeton Press (1941; JFM 67.0384.01)]. The gauge (Henstock-Kurzweil) integral [\textit{C. Swartz}, Introduction to gauge integrals. Singapore: World Scientific. (2001; Zbl 0982.26006)] is a generalization of Riemann, Lebesgue, Denjoy and Perron's integrals. In this paper, the authors consider the Laplace transform as a gauge integral. Using generalized differentiation, they obtain an inversion formula. Some elementary properties are given. The gauge Laplace transform of some functions are evaluated.
S. L. Kalla (Ellisville)
Zbl 0237.44001; Zbl 0920.44001; Zbl 0982.26006; JFM 67.0384.01