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Proceedings of the American Mathematical Society

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A criterion for the positivity of sine polynomials


Author: John Steinig
Journal: Proc. Amer. Math. Soc. 38 (1973), 583-586
MathSciNet review: 0310519
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Abstract | References | Additional Information

Abstract: A sufficient condition is derived for a sine polynomial with real coefficients to be nonnegative on $ (0,\pi )$.


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  • [1] Richard Askey, James Fitch, and George Gasper, On a positive trigonometric sum, Proc. Amer. Math. Soc. 19 (1968), 1507. MR 0231107, 10.1090/S0002-9939-1968-0231107-1
  • [2] Richard Askey, Positive Jacobi polynomial sums, Tôhoku Math. J. (2) 24 (1972), 109–119. Collection of articles dedicated to Gen-ichir\cflex o Sunouchi on his sixtieth birthday. MR 0340672
  • [3] L. Fejér, Über die positivität von Summen, die nach trigonometrischen oder Legendreschen Funktionen fortschreiten (erste Mitteilung), Acta Litt, ac Sci. Szeged 2 (1925), 75-86 (reproduced in Gesammelte Arbeiten II, Birkhäuser Verlag, Basel, 1970, pp. 128-138).
  • [4] -, Einige Sätze, die sich auf das Vorzeichen u.s.w., Monatsh. Math. Phys. 35 (1928), 305-344 (reproduced in Gesammelte Arbeiten II, 202-237).
  • [5] -, Über ein trigonometrisches Analogon eines Kakeyaschen Satzes, Jber. Deutsch. Math.-Verein. 38 (1929), 231-238 (reproduced in Gesammelte Arbeiten II, 256-263).
  • [6] Carl Hyltén-Cavallius, A positive trigonometrical kernel, Tolfte Skandinaviska Matematikerkongressen, Lund, 1953, Lunds Universitets Matematiska Institution, Lund, 1954, pp. 90–94. MR 0064897
  • [7] P. Turán, On a trigonometrical sum, Ann. Soc. Polon. Math. 25 (1952), 155–161 (1953). MR 0055475
  • [8] Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23. Revised ed, American Mathematical Society, Providence, R.I., 1959. MR 0106295


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0310519-3
Keywords: Trigonometric polynomials, Jacobi polynomials, positivity
Article copyright: © Copyright 1973 American Mathematical Society