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.
References
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.
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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