Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials

Sparse interpolation refers to the exact recovery of a function as short linear combination basis functions from limited number evaluations. For multivariate functions, case monomial is well studied, now exponential functions. Beyond Chebyshev polynomial obtained tensor products univariate polynomials, theory root systems allows define variety generalized polynomials that have connections topics such Fourier analysis and representations Lie algebras. We present deterministic algorithm recover at most r knowledge an explicitly bounded evaluations this function.