Begehr-Hile operator and its applications to some differential equations

Hua Liu; Zhaosheng Feng

doi:10.3934/cpaa.2010.9.387

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2010, Volume 9, Issue 2: 387-395. Doi: 10.3934/cpaa.2010.9.387

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Begehr-Hile operator and its applications to some differential equations

Hua Liu¹ and
Zhaosheng Feng^2,

1.
Department of Mathematics, Free University Berlin, Arnimallee 3, D-14195 Berlin
2.
Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539

Received: March 2008

Revised: November 2009

Published: March 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 30E25; Secondary: 47H30.

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