Fréchet frames for shift invariant weighted spaces

Suzana Simić

In the present paper we analyze Fréchet frame of the form $\{\varphi(\cdot-j)\mid j\in\mathbb Z^d\}$. With a known condition on $\varphi$, we show that the given sequence constitutes a frame for a test space isomorphic to the space of periodic smooth functions so that its dual is the multiple of the space of periodic distributions by $\hat\varphi$.