Pseudo-Laplace transform. (English) Zbl 0931.44001
Over certain semirings, pseudo-integrals are introduced and, in particular, corresponding convolutions, Laplace transforms and their inverses, which have the usual basic properties. The results are applied to problems in operations research (maximum of a utility function) and optimal control theory (solution of a Hamilton-Jacobi equation).
Reviewer: Lothar Berg (Rostock)
MSC:
| 44A10 | Laplace transform |
| 49J15 | Existence theories for optimal control problems involving ordinary differential equations |
| 91B16 | Utility theory |
Keywords:
pseudo-integrals; convolutions; Laplace transforms; inverses; operations research; utility function; optimal control; Hamilton-Jacobi equationReferences:
| [1] | J. Aczel, Lectures on Functional Equations and their Applications. Academic Press, New York, 1966.; J. Aczel, Lectures on Functional Equations and their Applications. Academic Press, New York, 1966. · Zbl 0139.09301 |
| [2] | Maslov, V. P., On a new superposition principle in optimization theory, Uspehi mat. nauk, 42, 39-48 (1987) · Zbl 0707.35138 |
| [3] | V.P. Maslov, S.N. Samborskij (Eds.), Idempotent Analysis, Advances in Soviet Mathematics 13. Amer. Math. Soc., Providence, RI, 1992.; V.P. Maslov, S.N. Samborskij (Eds.), Idempotent Analysis, Advances in Soviet Mathematics 13. Amer. Math. Soc., Providence, RI, 1992. |
| [4] | E. Pap, Null-Additive Set Functions. Kluwer Academic, Dordrecht, 1995.; E. Pap, Null-Additive Set Functions. Kluwer Academic, Dordrecht, 1995. · Zbl 0856.28001 |
| [5] | Pap, E., g-calculus, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat., 23, 1, 145-150 (1993) · Zbl 0823.28011 |
| [6] | D.V. Widder, The Laplace Transform. Princeton University Press, Princeton, 1946.; D.V. Widder, The Laplace Transform. Princeton University Press, Princeton, 1946. · Zbl 0060.24801 |
| [7] | R.E. Bellman, S.E. Dreyfus, Applied Dynamic Programming, Princeton University Press, Princeton, NJ, 1962.; R.E. Bellman, S.E. Dreyfus, Applied Dynamic Programming, Princeton University Press, Princeton, NJ, 1962. · Zbl 0106.34901 |
| [8] | R.E. Bellman, W. Karush, On a new functional transform in analysis: the Maximum Transform. Bull. Amer. Math. Soc. 67 (1961) 501-503.; R.E. Bellman, W. Karush, On a new functional transform in analysis: the Maximum Transform. Bull. Amer. Math. Soc. 67 (1961) 501-503. · Zbl 0103.09701 |
| [9] | Crandall, M. G.; Lions, P. L., Viscosity solutions of Hamilton-Jacobi equations,, Trans. Amer. Math. Soc., 272, 1-40 (1983) · Zbl 0599.35024 |
| [10] | P.L. Lions, Generalized Solutions of Hamilton-Jacobi equations. Pitman, London, 1982.; P.L. Lions, Generalized Solutions of Hamilton-Jacobi equations. Pitman, London, 1982. · Zbl 0497.35001 |
| [11] | Ralevic, N., Some new properties of g-calculus, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat., 24, 1, 139-157 (1994) · Zbl 0823.28012 |
| [12] | E. Pap, N. Teofanov, Pseudo-delta sequences, To Appear.; E. Pap, N. Teofanov, Pseudo-delta sequences, To Appear. |
| [13] | F. Baccelli, G. Cohen, G.J. Olsder, J.P. Quadrat, Synchronization and Linearity: an Algebra for Discrete Event Systems, Wiley, New York, 1992.; F. Baccelli, G. Cohen, G.J. Olsder, J.P. Quadrat, Synchronization and Linearity: an Algebra for Discrete Event Systems, Wiley, New York, 1992. · Zbl 0824.93003 |
| [14] | Sugeno, M.; Murofushi, T., Pseudo-additive measures and integrals, J. Math. Anal. Appl., 122, 197-222 (1987) · Zbl 0611.28010 |
| [15] | Fenchel, W., On the conjugate convex functions. Canadian Journal of Mathematics, 1, 73-77 (1949) · Zbl 0038.20902 |
| [16] | I. Ekeland, R. Temam, Convex analysis and variational problems. North-Holland, Amsterdam, 1976.; I. Ekeland, R. Temam, Convex analysis and variational problems. North-Holland, Amsterdam, 1976. · Zbl 0322.90046 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
