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# Begehr-Hile operator and its applications to some differential equations

• In the present paper, we are concerned with the integral hierarchy operator defined by Begehr and Hile in 1997. We show that the Begehr--Hile operator $T_{m,n}$ can be interpreted as the iteration of $T$ and $\bar {T}$ under certain conditions. Applications are also illustrated to some differential equations and singular integral equations in the complex plane.
Mathematics Subject Classification: Primary: 30E25; Secondary: 47H30.

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