Uniqueness and explicit form of Hermite–Chebyshev linear approximations

Relying on the known results on joint Hermite–Padé approximations of a system of trigonometric series, sufficient conditions are found under which linear Hermite–Chebyshev approximations exist and are determined uniquely. When the found conditions are met, the formulas are obtained that describe the explicit form of the numerators and denominator of linear Hermite–Padé approximations for a system of functions that are sums of Fourier series in Chebyshev polynomials of the first and second kind.