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Articles

On the order of rational Fourier coefficients of various bounded variations

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Pages 1737-1743 | Received 15 Apr 2012, Accepted 12 Jul 2012, Published online: 05 Oct 2012

References

  • Davis , HF . 1989 . Fourier Series and Orthogonal Functions , New York : Dover Publications .
  • Qian , T and Wang , YB . 2011 . Adaptive Fourier series-A variation of greedy algorithm . Adv. Comput. Math. , 34 ( 3 ) : 279 – 293 .
  • Qian , T , Zhang , LM and Li , ZX . 2011 . Algorithm of adaptive decomposition . IEEE Trans. Signal Proces. , 59 ( 10 ) : 4708 – 4718 .
  • Tan , LH , Shen , LX and Yang , LH . 2010 . Rational orthogonal bases satisfying the Bedrosian identity . Adv. Comput. Math. , 33 ( 3 ) : 285 – 303 .
  • Bultheel , A , González-Vera , P , Hendriksen , E and Njástad , O . 1999 . Orthogonal Rational Functions , New York : Cambridge University Press .
  • Akcay , H . 2001 . On the uniform approximation of discrete-time systems by generalized Fourier series . IEEE Trans. Signal Proces. , 49 ( 7 ) : 1461 – 1467 .
  • Ninness , B , Hjalmarsson , H and Gustafsson , F . 1999 . Generalized Fourier and Toeplitz results for rational orthonormal bases . SIAM J. Control Optim. , 37 ( 2 ) : 429 – 460 .
  • Vyas , RG . 2005 . A note on Fourier coefficients of functions of generalized Wiener class . Georgian Math. J. , 12 ( 3 ) : 535 – 538 .
  • Walterman , D . 1976 . On Λ-bounded variation . Stud. Math. , 57 : 33 – 45 .
  • Schramm , M and Waterman , D . 1982 . On the magnitude of Fourier coefficients . Proc. Am. Math. Soc. , 85 : 407 – 410 .
  • Fine , NJ . 1949 . On the Walsh functions . Trans. Am. Math. Soc. , 65 : 372 – 414 .
  • Izumi , M and Izumi , S . 1968 . Fourier series of functions of bounded variation . Proc. Japan Acad. , 44 : 415 – 417 .
  • Siddiqi , R . 1972 . The order of Fourier coefficients of function of higher variation . Proc. Japan Acad. , 48 : 569 – 572 .
  • Wiener , N . 1924 . The quadratic variation of a function and its Fourier coefficients . J. Math. Phys. , 3 : 72 – 94 .

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