Abstract
This chapter discusses the existence of local holomorphic solutions of differential equations of infinite order. Differential or microdifferential operators of infinite order are very important in studying the structure of partial differential equations of finite order. Also, differential equations of infinite order play a role in investigating theta functions. The chapter discusses some results concerning the existence of local holomorphic solutions of a differential equation of infinite order Pu=f, f being a given holomorphic function. Various theorems are also proven in the chapter.
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