Geodesic
Extremal Trigonometric and Power Polynomials in Several Variables
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 1, pp. 88-91

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We study extremal nonnegative polynomials in several variables. Our approach makes substantial use of block Toeplitz matrices. Note that the blocks of these matrices are themselves Toeplitz matrices.
Keywords: trigonometric polynomial, supporting hyperplane, convex set. 
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     author = {L. A. Sakhnovich},
     title = {Extremal {Trigonometric} and {Power} {Polynomials} in {Several} {Variables}},
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L. A. Sakhnovich. Extremal Trigonometric and Power Polynomials in Several Variables. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 1, pp. 88-91. http://geodesic.mathdoc.fr/item/FAA_2004_38_1_a9/