The estimation of the operational functions of the type exp[(Σ_{ν=1}^nβ_νs^{p_ν})λ]



Abstract

J. Mikusiński presented in the paper [2] the estimation of the operational function e-s^αλ, α∈(0,1), in some unbounded set of ℝ+×ℝ+. The results obtained by J. Mikusiński were generalized in the paper [3]. The similar estimation of the function
exp[(Σν=1nβνspν)λ]
is made in the above paper, where βν∈ℝ and pν∈(0.1), ν = 1,...,n.
This paper is devoted to the investigation of the behaviour more general operational functions, when the coefficients βν are in ℂ and fulfilling some relations concerning their real and imaginary parts.


1. J. Mikusiński, Operational calculus, PWN, Warszawa, 1967 (Reprinted Pergamon Press).
2. J. Mikusiński, Sur la croissance de la fonction operationelle exp(-s^αλ), Bull. Polish Acad. Sci. Math. 7 (1956), 423-425.
3. M. Piętka, A note on the increase of the operational function exp[(Σ_{k=1}^n A_k·s^{p_k})λ], Ann. Math. Sil. 3 (15) (1990), 107-114.
4. M. Piętka, Klasy jednoznaczności rozwiązań problemu Cauchy'ego dla równań różniczkowych cząstkowych i splotowych. Doctoral thesis, Katowice 1985.
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Published : 1990-09-28


PiętkaM. (1990). The estimation of the operational functions of the type exp[(Σ_{ν=1}^nβ_νs^{p_ν})λ]. Annales Mathematicae Silesianae, 4, 25-34. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14290

Marek Piętka 
Instytut Matematyki, Uniwersytet Śląski w Katowicach  Poland



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