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On gauge Laplace transform. (English) Zbl 1252.44001
The Laplace transform (Riemann integral) and the Laplace-Stieltjes transform (Lebesgue integral) have been studied by many authors [I. N. Sneddon, The use of integral transforms. New York etc.: McGraw-Hill Book Company. (1972; Zbl 0237.44001); L. Debnath, Integral transforms and their applications. Boca Raton, FL: CRC Press. (1995; Zbl 0920.44001); D. V. Widder, The Laplace transform. New York. Princeton Press (1941; JFM 67.0384.01)]. The gauge (Henstock-Kurzweil) integral [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.
##### MSC:
 44A10 Laplace transform 26A39 Denjoy and Perron integrals, other special integrals 44A20 Integral transforms of special functions
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