Decomposition of Spaces of Periodic Functions into Subspaces of Periodic and Antiperiodic Functions and Its Connection to the Rademacher System and the Haar Wavelet Basis

Hailu Bikila Yadeta

We prove that the space ${\mathbb{P}}_p$ of $p$-periodic functions decomposes as the direct sum ${\mathbb{P}}_{p/2}\oplus \mathbb{A}{\mathbb{P}}_{p/2}$, where ${\mathbb{P}}_{p/2}$ denotes…