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Incompleteness and closure of the multiplicity system {t(k)e(lambda)j(t)} in the weighted Banach space

Abstract: We investigate the completeness, closure and minimalty of the multiplicity system M(Lambda) = {t(k)e(lambda nt): k = 0, 1, 2,..., mu(n) - 1; n = 1, 2....} in the weighted Banach space C-alpha, where the sequence Lambda = {lambda(n), mu(n)}(n=1)(infinity) and (n = 1, 2,...) are distinct complex numbers in the right half-plane satisfying vertical bar lambda(n)vertical bar < vertical bar lambda(n+1)vertical bar (n = 1, 2....) and increasing to infinity, each lambda(n) appears mu(n) times with mu(n) not necessarily bounded.