sine型函数和样本定理

SINE FUNCTIONS AND THE SAMPLING THEOREM

证明了Bπ ,p,1<p <∞中函数在sine型函数的零点上Marcinkiewicz Zygmund型不等式 ,并对经典的Whittaker Kotelnikov Shannon样本定理作了推广 ,得出Bπ ,p中函数可以由sine型函数的零点组成的节点组上的值在点态及Lp

A Marcinkiewicz Zygmund type inequality of bandlimited functions is proved.Moreover, it is proved that the bandlimited functions can be reconstructed in L p (R) by interpolation at irregular spaced nodes which satisfy some conditions.