一类混合指数型积分算子的整体饱和定理
A Global Saturation Theorem for the Mixed Exponential Type Integral Operators
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摘要: 引入了一类广义指数型积分算子,称其为混合指数型积分算子。研究了该类混合指数型积分算子的性 质,利用改进的Bajsanski-Bojanic抛物线技巧及积分算子的有关性质,建立了一类混合指数型积分算子的整体饱 和定理。这样,包含Baskakov型在内的相关积分算子的饱和结果便可以很容易得到,为研究混合指数型积分算 子的逼近转化定理奠定了基础,也为研究算子的饱和问题提供了新的方法。Abstract: A general exponential type integral operator, called mixed exponential type integral operator, is introduced, and the properties of this type of integral operator are studied. Based on the improved Bajsanski-Bojanic parabolic method and the related properties of integral operators, a global saturation theorem for the mixed exponential type integral operatorLnis established. So, the saturation results of some operators including Baskakov operator can be obtained easily, hence laying a basis for studying the approximation transformation theoremof the mixed exponential type integral operators, and presenting a new method for studying the saturation problems.
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