March  2010, 9(2): 387-395. doi: 10.3934/cpaa.2010.9.387

Begehr-Hile operator and its applications to some differential equations

1. 

Department of Mathematics, Free University Berlin, Arnimallee 3, D-14195 Berlin, Germany

2. 

Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539

Received  March 2008 Revised  November 2009 Published  December 2009

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.
Citation: Hua Liu, Zhaosheng Feng. Begehr-Hile operator and its applications to some differential equations. Communications on Pure and Applied Analysis, 2010, 9 (2) : 387-395. doi: 10.3934/cpaa.2010.9.387
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