## Orthogonal Trigonometric Sums with Auxiliary Conditions |

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### Contents

Construction of the System of Trigonometric Sums 8 | 8 |

H Exceptional Values of the Subscript | 14 |

Recursion Formulas | 19 |

4 other sections not shown

### Common terms and phrases

American Mathematical Society arbitrary constant arbitrary function augmented matrix auxiliary conditions Christoffel-Darboux Identities coefficients continuous function convergence corresponding defined different from zero entire interval equations exceptional values expressible in terms f p(t finite number Fourier Series func function f(x Hence identically zero integrability of p(t interval of length Jackson liary conditions number of points obtained orthogonal functions Orthogonal Polynomials Orthogonal Trigonometric Sums orthonormal system orthonormal with respect period interval positive measure recursion formula respect to p(t results of Section s s s satisfying the auxiliary satisfying the conditions sequence series 28 set of points sets E1 siné Sn(x specified value subscript sum of order sum s(t summable suns un(x theorem tion trigono trigonometric sum satisfying uk(x un(t uniformly bounded vh(x vk(x vn(t vn(x weight function zeros of s(t