A property of subspaces admitting spectral synthesis

Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis

“…1. Inequalities ln | ( )| | |, ln | ( )| | | for | | ( /∆) max{| |, | |} can be proven in the same way as Item 1 of Lemma 1 in [6] taking into consideration conditions (3.4) for number ∆ and ordering of sequences Λ and Γ by ascending | |, | |.…”

“…In particular, it allows one to obtain statements on 2-generated or representation by a sum of two special local submodules (ideals) for local submodules (cf. [6]- [11]), or sometimes, like in our case, only for stable submodules (Theorem 2).…”

“…2. To prove estimates (3.6) and (3.7) we make use the scheme employed in the proof of Items 2 and 3 of Lemma 1 in [6]. We fix arbitrary ∈ (0; 1/2).…”

“…The sufficient condition for stability of submodule with two generators provided in Theorem 1 seem to be far from necessary as in all statements of this kind we know (cf. [6]- [11]). On the other hand, in contrast to the general criterion of I.F.…”

On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis

“…The issue on 2-degenerateness in a wide sense was studied earlier for localizable (ample) submodules in the module of entire functions of finite order determined by restrictions for the indicator [10], [11], for localized (ample) submodules in abstract weighted submodules of holomorphic functions [12], for submodules with a finite zero set in the module ( ; ) [4]. One of the results of work [12] is the theorem stating that localizable (ample) submodules of the module ( ; ) are generated by two submodules of the form ( , ( ; )).…”