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We prove Nehari s theorem for integral Hankel and Toeplitz operators on simple convex polytopes in several variables. A special case of the theorem, generalizing the boundedness criterion of the Hankel and Toeplitz operators on the Paley Wiener space, reads as follows. Let = (0, 1)d be a d-dimensional cube, and for a distribution f on 2, consider the Hankel operator f (g)(x) = λ f (x + y)g(y) dy,
