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The aim of this article is to show the existence, and also give an explicitconstruction, of infinite sets of orthogonal exponentials for certain familiesof convex polytopes which include simple-rational polytopes and also non simplepolytopes which satisfy other nontrivial conditions. We also show that byconsidering weight functions one can construct infinite sets of orthogonalexponentials with a positive density by considering orthogonal projections ofaffine transformations of hypercubes (i.e., zonotopes).

Constructing Infinite Sets of Orthogonal Exponentials for Convex Polytopes