Recovering functions from the modulation spaces FW

الأصل · EN

In this short note we show that functions in the modulation space FW={ f: ∑jⁿ f(·+2πj)ₗ∞₍[₋π,π]ₙ₎<∞ } enjoy similar recovery properties as band-limited functions. If {ϕα} is a regular family of cardinal interpolators, then one can build an approximand of f using the fundamental functions corresponding to ϕα. Then taking the appropriate limit, one recovers f both in norm and pointwise.