Basis property of families of Mittag-Leffler-type functions, the dzhrbashyan transformations, and the muckenhoupt condition

Unconditional bases in 𝐿²(0,𝑎)

“…We observe first that h(z -A")_1 G H2 in view of Lemma 1. Now we show how to deduce the main result of [5] PROOF. This theorem is in fact a partial case of Theorem 1 with h = z1~13.…”

“…The methods developed in [1 and 3] can be applied to the description of the resonance frequences of semi-infinite strings corresponding to unconditional bases of resonance states [4]. One more application has been considered recently in [5] to investigate the unconditional basis property of{xP-1Eit0(ixXn)} in L2(0,a). Here…”

“…In this paper the results of [5] are extended to more general families. The advantage of the approach presented is that it makes the arguments more transparent even in the case of exponentials (ß = 1).…”