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Abstract: The one-dimensional Dunkl operator $D k$ with a non-negative parameter $k$,is considered under an arbitrary nonlocal boundary value condition. The rightinverse operator of $D k$, satisfying this condition is studied. An operationalcalculus of Mikusinski type is developed. In the frames of this operationalcalculi an extension of the Heaviside algorithm for solution of nonlocal Cauchyboundary value problems for Dunkl functional-differential equations $PD ku=f$with a given polynomial $P$ is proposed. The solution of these equations inmean-periodic functions reduces to such problems. Necessary and sufficientcondition for existence of unique solution in mean-periodic functions is found.



Autor: Ivan H. Dimovski, Valentin Z. Hristov

Fuente: https://arxiv.org/



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