On absence conditions of unconditional bases of exponents
Rustem Abdraufovich Bashmakov, Alla Aleksandrovna Makhota, Kirill Vladimirovich Trounov Β· Ufimskii Matematicheskii Zhurnal Β· 2015
In the classical space πΏ 2 (-π, π) there exists the unconditional basis {π πππ‘ } (π is integer).In the work we study the existence of unconditional bases in weighted Hilbert spaces πΏ 2 (πΌ, exp β) of the functions square integrable on an interval πΌ in the real axis with the weight exp(-β), where β is a convex function.We obtain conditions showing that unconditional bases of exponents can exist only in very rare cases.