q-Laplace Transforms
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초록
Two q-analogues of the well-known Laplace transform are defined with the help of the Jackson integral. In this paper, firstly q-convolution the- orem for qLs operator is studied. Some convolution examples are obtained and also [수식] is proved via q-convolution theorem. [수식] is found for some elementary functions. Fi- nally, [수식] is obtained in terms of [수식]. Furthermore, [수식] and [수식] are de…ned and some properties of [수식] and [수식] are proved.
Abstract
Two q-analogues of the well-known Laplace transform are defined with the help of the Jackson integral. In this paper, firstly q-convolution the- orem for qLs operator is studied. Some convolution examples are obtained and also [수식] is proved via q-convolution theorem. [수식] is found for some elementary functions. Fi- nally, [수식] is obtained in terms of [수식]. Furthermore, [수식] and [수식] are de…ned and some properties of [수식] and [수식] are proved.
참고문헌 (6)
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- Abdi, W.H, "On q-Laplace Transforms", Proc. Nat. Acad. Sci. India, 29, pp.389~408 (1961)
- Gasper , G, "Lecture Notes For An Introductory Minicourse on q-Series", ~ (1995)
- Hahn, W, "Beiträge zur Theorie der Heineschen Reihen", Math. Nachr., 2, pp.340~379 (1949)
- Sneddon, I N, "The Use of Integral Transforms" (1972), McGraw-Hill
- Yürekli, O, "A Theorem on The Generalized Stieltjes Transform and Its Applications", J. Math. Anal. Appl., 168, pp.63~71 (1992)