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J. Sib. Fed. Univ. Math. Phys., 2008, Volume 1, Issue 4, Pages 371–379 (Mi jsfu37)  

This article is cited in 4 scientific papers (total in 4 papers)

Generalized Convolutions for the Fourier Integral Transforms and Applications

Bui Thi Gianga, Nguyen Minh Tuanb

a Department of Basic Science, Institute of Cryptography Science, Hanoi, Vietnam
b Department of Mathematical Analysis, University of Hanoi, Hanoi, Vietnam

Abstract: This paper provides some generalized convolutions for the Fourier integral transforms and treats the applications. Namely, there are six generalized convolutions with weight-function for the Fourier integral transforms. As for applications, the normed ring structures on $L^1(\mathbb R^d)$ are constructed, and the explicit solution in $L^1(\mathbb R^d)$ of the integral equations with the mixed Toeplitz–Hankel kernel are obtained.

Keywords: generalized convolution, normed ring, integral equation of convolution type.

Full text: PDF file (309 kB)
References: PDF file   HTML file
UDC: 517.5
Received: 15.09.2008
Received in revised form: 20.10.2008
Accepted: 15.11.2008
Language:

Citation: Bui Thi Giang, Nguyen Minh Tuan, “Generalized Convolutions for the Fourier Integral Transforms and Applications”, J. Sib. Fed. Univ. Math. Phys., 1:4 (2008), 371–379

Citation in format AMSBIB
\Bibitem{BuiNgu08}
\by Bui~Thi~Giang, Nguyen~Minh~Tuan
\paper Generalized Convolutions for the Fourier Integral Transforms and Applications
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2008
\vol 1
\issue 4
\pages 371--379
\mathnet{http://mi.mathnet.ru/jsfu37}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Giang Bui Thi, Mau Nguyen Van, Tuan Nguyen Minh, “Operational properties of two integral transforms of Fourier type and their convolutions”, Integral Equations Operator Theory, 65:3 (2009), 363–386  crossref  mathscinet  zmath  isi  elib
    2. Bui Thi Giang, Nguyen Van Mau, Nguyen Minh Tuan, “Convolutions for the Fourier transforms with geometric variables and applications”, Math. Nachr., 283:12 (2010), 1758–1770  crossref  mathscinet  zmath  isi
    3. Tuan Nguyen Minh, Huyen Nguyen Thi Thu, “The solvability and explicit solutions of two integral equations via generalized convolutions”, J. Math. Anal. Appl., 369:2 (2010), 712–718  crossref  mathscinet  zmath  isi  elib
    4. Nguyen Minh Tuan, Nguyen Thi Thu Huyen, “Applications of Generalized Convolutions Associated with the Fourier and Hartley Transforms”, J. Integral Equ. Appl., 24:1 (2012), 111–130  crossref  mathscinet  zmath  isi
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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