Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지

LARGE SIEVE FOR GENERALIZED TRIGONOMETRIC POLYNOMIALS

  • Published : 1999.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

Generalized nonnegative trigonometric polynomials are defined as the products of nonnegative trigonometric polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We improve and extend the large sieve involving pth powers of trigonometric polynomials so that it holds for generalized trigonometric polynomials.

Keywords

References

  1. Kexue Tongbao v.17 On the representation of a large even integer as the sum of a prime and the product of at most two primes J. Chen
  2. Sci. Sinica v.16 On the representation of a large even integer as the sum of a prime and the product of at most two primes J. Chen
  3. Can. J. Math. v.43 Bernstein and Markov type inequalities for generalized non-negative polynomials T. Erdelyi
  4. J. London Math. Soc. v.45 Remez-type inequalities on the size of generalized non-negative polynomials T. Erdelyi
  5. Constr. Approx. v.8 Inequalities for generalized nonnegative polynomials T. Erdelyi;A. Mate;P. Nevai
  6. J. Approx. Theory v.69 Generalized Jacobi weights, Christoffel functions and zeros of orthogonal polynomials T. Erdelyi;P. Nevai
  7. Dokl. Akad. Nauk SSSR v.30 The large sieve Ju. V. Linnik
  8. Siam J. Math. Anal. v.18 Quadrature sums involving pth powers of polynomials D. S. Lubinsky;A. Mate;P. Nevai
  9. Bull. Amer. Math. Soc. v.84 The analytic principle of the large sieve H. L. Montgomery
  10. Ann. of Math. v.111 Bernstein's inequality in $L^p $ for 0 < p < 1 and (C, 1) bounds for orthogonal polynomials A. Mate;P. Nevai
  11. Dokl. Akad. Nauk SSSR v.56 On the representation of an even number as the sum of a single prime and a single almost-prime number A. Renyi
  12. Izv. Akad. Nauk SSSR Ser. Mat. v.12 On the representation of an even number as the sum of a single prime and a single almost-prime number A. Renyi
  13. Trigonometric Series, 1 A. Zygmund