Author： Dimovski Ivan Hristov Valentin
Publisher： Taylor & Francis Ltd
ISSN： 1065-2469
Source： Integral Transforms and Special Functions, Vol.18, Iss.2, 2007-01, pp. : 117-131
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Abstract
The Euler operator δ=t(d/dt) is considered in the space C=C(+), +=(0, ∞), and the operators M: C→C such that Mδ=δ M in C1(+) are characterized. Next, for a non-zero linear functional Φ: C(+)→ the continuous linear operators M with the invariant hyperplane Φ{f}=0 and commuting with δ in it are also characterized. Further, mean-periodic functions for δ with respect to the functional Φ are introduced and it is proved that they form an ideal in a corresponding convolutional algebra (C(+), *). As an application, unique mean-periodic solutions of Euler differential equations are characterized.
Related content
Access to resources
Recommend
ON WEIGHTED INEQUALITIES WITH GEOMETRIC MEAN OPERATOR
Bulletin of the Australian Mathematical Society, Vol. 78, Iss. 3, 2008-12 ,pp. :