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Let Πn = Πn(it, cosα), where n ≧ 2 is an integer, t ≠ 0 is real and 0 ≦ α ≦ π, be the class of trigonometrical polynomials Φn with real coefficients and of order ≦ n, such that |Φn(x)| ≦ 1 for all ...

In this paper we use a set of partial differential equations to prove an expansion theorem for multiple complex Hermite polynomials. This expansion theorem allows us to develop a systematic and ...