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Estimates of the norms of some cosine and sine series

Yıl 2023, , 142 - 150, 15.09.2023
https://doi.org/10.33205/cma.1345440

Öz

In the work we estimate the $\mathbb{L}^1$ norms of some special cosine and sine series used in studying fractional integrals.

Kaynakça

  • N. K. Bari: Trigonometric Series, Moscow (in Russian, 1961).
  • R. G. Bartle: The Elements of Integration, John Wiley and Sons, Inc., New York-London-Sydney (1966).
  • A. S. Belov: On the unimprovability of some theorems on the convergence in the mean of trigonometric series, J. Math. Sci. (N.Y.), 250(3) (2020), 404–418.
  • G. Brown, K. Y. Wang and D. C. Wilson: Positivity of some basic cosine sums, Math. Proc. Cambridge Philos. Soc., 114(3) (1993), 383–391.
  • P. L. Butzer, R. J. Nessel: Fourier Analysis and Approximation, New York-Basel (1971).
  • P. L. Butzer, U.Westphal: An access to fractional differentiation via fractional difference quotients, Fractional Calculus and Its Applications, Lecture Notes in Mathematics, 457 (1975), 116–145.
  • J. W. Garrett, Cˇ . V. Stanojevic´: Necessary and sufficient conditions for $\mathbb{L}^1$ convergence of trigonometric series, Proc. Amer. Math. Soc., 60 (1976), 68–71.
  • J.W. Garrett, Cˇ . V. Stanojevic´: On $\mathbb{L}^1$ convergence of certain cosine sums, Proc. Amer.Math. Soc., 54 (1976), 101–105.
  • M. Izumi, Sh. Izumi: On some trigonometrical polynomials, Math. Scand., 21 (1967), 38–44.
  • I. P. Natanson: Constructive Function Theory. Vol I, Frederick Ungar Publ., New York (1964).
  • B. Szal: On L-convergence of trigonometric series, J. Math. Anal. Appl., 373(2) (2011), 449–463.
  • Z. Tomovski: Convergence and integrability for some classes of trigonometric series, Dissertationes Math (Rozprawy Mat.), 420 (2003), 65 pp.
  • W. H. Young: On a certain series of Fourier, Proc. London Math. Soc., 11 (1913), 357–366.
  • A. Zygmund: Trigonometric series, Third Edition, Vol I and II combined, Cambridge Mathematical Library (2002).
Yıl 2023, , 142 - 150, 15.09.2023
https://doi.org/10.33205/cma.1345440

Öz

Kaynakça

  • N. K. Bari: Trigonometric Series, Moscow (in Russian, 1961).
  • R. G. Bartle: The Elements of Integration, John Wiley and Sons, Inc., New York-London-Sydney (1966).
  • A. S. Belov: On the unimprovability of some theorems on the convergence in the mean of trigonometric series, J. Math. Sci. (N.Y.), 250(3) (2020), 404–418.
  • G. Brown, K. Y. Wang and D. C. Wilson: Positivity of some basic cosine sums, Math. Proc. Cambridge Philos. Soc., 114(3) (1993), 383–391.
  • P. L. Butzer, R. J. Nessel: Fourier Analysis and Approximation, New York-Basel (1971).
  • P. L. Butzer, U.Westphal: An access to fractional differentiation via fractional difference quotients, Fractional Calculus and Its Applications, Lecture Notes in Mathematics, 457 (1975), 116–145.
  • J. W. Garrett, Cˇ . V. Stanojevic´: Necessary and sufficient conditions for $\mathbb{L}^1$ convergence of trigonometric series, Proc. Amer. Math. Soc., 60 (1976), 68–71.
  • J.W. Garrett, Cˇ . V. Stanojevic´: On $\mathbb{L}^1$ convergence of certain cosine sums, Proc. Amer.Math. Soc., 54 (1976), 101–105.
  • M. Izumi, Sh. Izumi: On some trigonometrical polynomials, Math. Scand., 21 (1967), 38–44.
  • I. P. Natanson: Constructive Function Theory. Vol I, Frederick Ungar Publ., New York (1964).
  • B. Szal: On L-convergence of trigonometric series, J. Math. Anal. Appl., 373(2) (2011), 449–463.
  • Z. Tomovski: Convergence and integrability for some classes of trigonometric series, Dissertationes Math (Rozprawy Mat.), 420 (2003), 65 pp.
  • W. H. Young: On a certain series of Fourier, Proc. London Math. Soc., 11 (1913), 357–366.
  • A. Zygmund: Trigonometric series, Third Edition, Vol I and II combined, Cambridge Mathematical Library (2002).
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Lie Grupları, Harmonik ve Fourier Analizi
Bölüm Makaleler
Yazarlar

Jorge Bustamante 0000-0003-2856-6738

Erken Görünüm Tarihi 18 Ağustos 2023
Yayımlanma Tarihi 15 Eylül 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Bustamante, J. (2023). Estimates of the norms of some cosine and sine series. Constructive Mathematical Analysis, 6(3), 142-150. https://doi.org/10.33205/cma.1345440
AMA Bustamante J. Estimates of the norms of some cosine and sine series. CMA. Eylül 2023;6(3):142-150. doi:10.33205/cma.1345440
Chicago Bustamante, Jorge. “Estimates of the Norms of Some Cosine and Sine Series”. Constructive Mathematical Analysis 6, sy. 3 (Eylül 2023): 142-50. https://doi.org/10.33205/cma.1345440.
EndNote Bustamante J (01 Eylül 2023) Estimates of the norms of some cosine and sine series. Constructive Mathematical Analysis 6 3 142–150.
IEEE J. Bustamante, “Estimates of the norms of some cosine and sine series”, CMA, c. 6, sy. 3, ss. 142–150, 2023, doi: 10.33205/cma.1345440.
ISNAD Bustamante, Jorge. “Estimates of the Norms of Some Cosine and Sine Series”. Constructive Mathematical Analysis 6/3 (Eylül 2023), 142-150. https://doi.org/10.33205/cma.1345440.
JAMA Bustamante J. Estimates of the norms of some cosine and sine series. CMA. 2023;6:142–150.
MLA Bustamante, Jorge. “Estimates of the Norms of Some Cosine and Sine Series”. Constructive Mathematical Analysis, c. 6, sy. 3, 2023, ss. 142-50, doi:10.33205/cma.1345440.
Vancouver Bustamante J. Estimates of the norms of some cosine and sine series. CMA. 2023;6(3):142-50.