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What Is Variable Bandwidth?

We propose a new notion of variable bandwidth that is based on the spectral subspaces of an elliptic operator Apf=−ddx(p(x)ddx)f where p > 0 is a strictly positive function. Denote by cΛ(Ap) the orthogonal projection of Ap corresponding to the spectrum of Ap in Λ⊂ ℝ+ ; the range of this projection is the space of functions of variable bandwidth with spectral set in Λ.