Generalized Laplace transform of locally integrable functions defined on [0,∞)
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In [Bull. Cl. Sci. Math. Nat. Sci. Math. 40 (2015), 99 − 113] we defined
the Laplace transform on a bounded interval [0, b], denoted by 0L, using some ideas of H.
Komatsu [J. Fac. Sci. Univ. Tokyo, IA, 34 (1987), 805–820] and [Structure of solutions
of differential equations (Katata/Kyoto, 1995), pp. 227–252, World Sci. Publishing, River
Edge, NJ, 1996]. We use this definition to extend it to the space of locally integrable functions
defined on [0,1), which is a wider class then functions L used by G. Doetsch [Handbuch der
Lalace-Transformation I, Basel – Stuttgart, 1950 − 1956, p. 32]. As an application we give
solutions of integral equations of the convolution type, defined on a bounded interval, or on
the half-axis as well, and of equations with fractional derivatives.
Keywords:
Space of locally integrable functions / Laplace transform of functions belonging to L[0, b], 0 < b <∞ ; / Laplace transform of locally integrable functions [0,∞).Source:
Bulletin T.CL de l’Académie serbe des sciences et des arts, 2017, 41-52Publisher:
- Beograd : Académie Serbe des sciences et des arts
Note:
- Bulletin t. 150 de l'Académie serbe des sciences et des arts. Classe des sciences mathématiques et naturelles. Sciences mathematiques no 42.
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Cрпска академија наука и уметности / Serbian Academy of Sciences and ArtsTY - JOUR AU - Stanković, Bogoljub PY - 2017 UR - https://dais.sanu.ac.rs/123456789/16442 AB - In [Bull. Cl. Sci. Math. Nat. Sci. Math. 40 (2015), 99 − 113] we defined the Laplace transform on a bounded interval [0, b], denoted by 0L, using some ideas of H. Komatsu [J. Fac. Sci. Univ. Tokyo, IA, 34 (1987), 805–820] and [Structure of solutions of differential equations (Katata/Kyoto, 1995), pp. 227–252, World Sci. Publishing, River Edge, NJ, 1996]. We use this definition to extend it to the space of locally integrable functions defined on [0,1), which is a wider class then functions L used by G. Doetsch [Handbuch der Lalace-Transformation I, Basel – Stuttgart, 1950 − 1956, p. 32]. As an application we give solutions of integral equations of the convolution type, defined on a bounded interval, or on the half-axis as well, and of equations with fractional derivatives. PB - Beograd : Académie Serbe des sciences et des arts T2 - Bulletin T.CL de l’Académie serbe des sciences et des arts T1 - Generalized Laplace transform of locally integrable functions defined on [0,∞) SP - 41 EP - 52 UR - https://hdl.handle.net/21.15107/rcub_dais_16442 ER -
@article{ author = "Stanković, Bogoljub", year = "2017", abstract = "In [Bull. Cl. Sci. Math. Nat. Sci. Math. 40 (2015), 99 − 113] we defined the Laplace transform on a bounded interval [0, b], denoted by 0L, using some ideas of H. Komatsu [J. Fac. Sci. Univ. Tokyo, IA, 34 (1987), 805–820] and [Structure of solutions of differential equations (Katata/Kyoto, 1995), pp. 227–252, World Sci. Publishing, River Edge, NJ, 1996]. We use this definition to extend it to the space of locally integrable functions defined on [0,1), which is a wider class then functions L used by G. Doetsch [Handbuch der Lalace-Transformation I, Basel – Stuttgart, 1950 − 1956, p. 32]. As an application we give solutions of integral equations of the convolution type, defined on a bounded interval, or on the half-axis as well, and of equations with fractional derivatives.", publisher = "Beograd : Académie Serbe des sciences et des arts", journal = "Bulletin T.CL de l’Académie serbe des sciences et des arts", title = "Generalized Laplace transform of locally integrable functions defined on [0,∞)", pages = "41-52", url = "https://hdl.handle.net/21.15107/rcub_dais_16442" }
Stanković, B.. (2017). Generalized Laplace transform of locally integrable functions defined on [0,∞). in Bulletin T.CL de l’Académie serbe des sciences et des arts Beograd : Académie Serbe des sciences et des arts., 41-52. https://hdl.handle.net/21.15107/rcub_dais_16442
Stanković B. Generalized Laplace transform of locally integrable functions defined on [0,∞). in Bulletin T.CL de l’Académie serbe des sciences et des arts. 2017;:41-52. https://hdl.handle.net/21.15107/rcub_dais_16442 .
Stanković, Bogoljub, "Generalized Laplace transform of locally integrable functions defined on [0,∞)" in Bulletin T.CL de l’Académie serbe des sciences et des arts (2017):41-52, https://hdl.handle.net/21.15107/rcub_dais_16442 .