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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 6, Pages 939–945 (Mi zvmmf4570)  

This article is cited in 10 scientific papers (total in 10 papers)

Some remarks concerning the Fourier transform in the space $L_2(\mathbb R)$

V. A. Abilova, F. V. Abilovab, M. K. Kerimovc

a Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia
b Dagestan State Technical University, pr. Kalinina 70, Makhachkala, 367015, Russia
c Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: Two useful estimates are proved for the Fourier transform in the space of square integrable functions on certain classes of functions characterized by the generalized continuity modulus.

Key words: integral Fourier transform, generalized derivatives, Steklov function.

Full text: PDF file (547 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2008, 48:6, 885–891

Bibliographic databases:

UDC: 519.651
Received: 01.10.2007
Revised: 14.01.2008

Citation: V. A. Abilov, F. V. Abilova, M. K. Kerimov, “Some remarks concerning the Fourier transform in the space $L_2(\mathbb R)$”, Zh. Vychisl. Mat. Mat. Fiz., 48:6 (2008), 939–945; Comput. Math. Math. Phys., 48:6 (2008), 885–891

Citation in format AMSBIB
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\paper Some remarks concerning the Fourier transform in the space $L_2(\mathbb R)$
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\pages 939--945
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Abilov, F. V. Abilova, M. K. Kerimov, “Some remarks concerning the Fourier transform in the space $L_2(\mathbb R^n)$”, Comput. Math. Math. Phys., 48:12 (2008), 2146–2153  mathnet  crossref  mathscinet  isi
    2. V. A. Abilov, F. V. Abilova, M. K. Kerimov, “On estimates for the Fourier-Bessel integral transform in the space $L_2(\mathbb R_+)$”, Comput. Math. Math. Phys., 49:7 (2009), 1103–1110  mathnet  crossref  isi  elib  elib
    3. V. A. Abilov, F. V. Abilova, M. K. Kerimov, “Some new estimates of the Fourier transform in $\mathbb{L}_2(\mathbb{R})$”, Comput. Math. Math. Phys., 53:9 (2013), 1231–1238  mathnet  crossref  crossref  isi  elib  elib
    4. V. A. Abilov, F. V. Abilova, M. K. Kerimov, “Some new estimates of the Fourier–Bessel transform in the space $\mathbb{L}_2(\mathbb{R}_+)$”, Comput. Math. Math. Phys., 53:10 (2013), 1440–1446  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. El Hamma M., Daher R., “Dini Lipschitz Functions For the Dunkl Transform in the Space l-2(R-D, W(K)(X)Dx)”, Rend. Circ. Mat. Palermo, 64:2 (2015), 241–249  crossref  mathscinet  zmath  isi  scopus
    6. El Ouadih S., Daher R., “Some new estimates for the Cherednik–Opdam transform in the space
      $$L^{2}_{\alpha ,\beta }(\mathbb {R})$$
      L , 2 ( R )”, J. Pseudo-Differ. Oper. Appl., 7:1 (2016), 47–58  crossref  mathscinet  zmath  isi  scopus
    7. El Ouadih S., Daher R., “New Estimates For the Generalized Fourier-Bessel Transform in the Space l-Alpha,N(2)”, Southeast Asian Bull. Math., 41:2 (2017), 209–218  mathscinet  zmath  isi
    8. Daher R., El Ouadih S., Lafdal H.S., “On Estimates For the Generalized Fourier-Dunkl Transform in the Space l-Alpha,N(2)”, Matematika, 34:1 (2018), 153–161  crossref  mathscinet  isi
    9. Daher R., El Ouadih S., “Some New Estimates For the Helgason Fourier Transform on Rank 1 Symmetric Spaces”, Proc. Indian Acad. Sci.-Math. Sci., 128:3 (2018), UNSP 37  crossref  mathscinet  isi  scopus
    10. S. El Ouadih, R. Daher, H. S. Lafdal, “Some estimates for the generalized Fourier transform associated with the Cherednik–Opdam operator on $\mathbb{R}$”, Vladikavk. matem. zhurn., 20:3 (2018), 78–86  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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