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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.
44A10 Laplace transform
26A39 Denjoy and Perron integrals, other special integrals
44A20 Integral transforms of special functions
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