Incompleteness and closure of the multiplicity system {tkeλjt} in the weighted Banach space

We investigate the completeness, closure and minimalty of the multiplicity system in the weighted Banach space Cα, where the sequence and {λn} (n=1,2,…) are distinct complex numbers in the right half-plane satisfying |λn|<|λn+1| (n=1,2,…) and increasing to infinity, each λn appears μn times with μn not necessarily bounded.