一类空间中高阶微分的性质

The properties of higher-order derivative in a class of Banach spaces

对具有Schauder基的无穷维Banach空间上的映射定义高阶偏导数 ,讨论其高阶微分与高阶偏导数的关系 ,并讨论映射的像所在空间为具有Schauder基的无穷维Banach空间时 。

Partial derivative is defined for a map f in Banach space with schauder base.Then the relationship between higher-order differentiable property of f and existence of higer-order partial derivative of f is discussed.Also the relationship between f and its coordinate functions f i about higher-order differential is analyzed when the image space with schauder base.