Unconditional bases in 𝐿²(0,𝑎)

Abstract

ABSTRACT.A method is given for producing unconditional bases in subspaces Kg = H2 Q 9H2 of the Hardy space H2, 9 being an inner function in the upper half-plane.For 9 = exp(iaz) the space Kg is the Fourier-Laplace transform of L2(0,a), which allows us to establish a necessary and sufficient condition for certain families of functions (including exponentials) to constitute unconditional bases in L2(0,a).