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Mat. Zametki, 2004, Volume 76, Issue 1, Pages 20–26 (Mi mz85)  

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

On Polyconvolutions Generated by the Hankel Transform

L. E. Britvina

Novgorod State University after Yaroslav the Wise

Abstract: In this paper, we construct two polyconvolutions (generalized convolutions) with weight $\gamma=x^{-\nu}$ generated by the Hankel transform possessing the factorization relations
$$ H_\nu[h_1](x)=x^{-\nu}H_\mu[f](x)H_\mu[g](x), \qquad H_\mu[h_2](x)=x^{-\nu}H_\nu[f](x)H_\mu[g](x). $$
Here $H_\mu$ is the Hankel transform operator of order $\mu$. Conditions for the existence of the constructed polyconvolutions are found. On their basis, using the differential properties of the Hankel transform, we obtain two more polyconvolutions. The derived constructions allow us to solve new classes of integral and integro-differential equations and systems of equations.

DOI: https://doi.org/10.4213/mzm85

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English version:
Mathematical Notes, 2004, 76:1, 18–24

Bibliographic databases:

UDC: 517.9
Received: 25.06.2001

Citation: L. E. Britvina, “On Polyconvolutions Generated by the Hankel Transform”, Mat. Zametki, 76:1 (2004), 20–26; Math. Notes, 76:1 (2004), 18–24

Citation in format AMSBIB
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\by L.~E.~Britvina
\paper On Polyconvolutions Generated by the Hankel Transform
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\yr 2004
\vol 76
\issue 1
\pages 20--26
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\vol 76
\issue 1
\pages 18--24
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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. Britvina L.E., “Generalized convolutions for the Hankel transform and related integral operators”, Math. Nachr., 280:9-10 (2007), 962–970  crossref  mathscinet  zmath  isi  elib  scopus
    2. Britvina L.E., “Integral operators related to generalized convolutions for Hankel transform”, Integral Transforms Spec. Funct., 20:9-10 (2009), 785–796  crossref  mathscinet  zmath  isi  elib  scopus
    3. Phi Thi Van Anh, Nguyen Xuan Thao, “Inequalities for the Hartley-Fourier cosine polyconvolution”, Math. Inequal. Appl., 19:3 (2016), 1049–1066  crossref  mathscinet  zmath  isi  scopus
    4. Britvina L.E., “Generalized convolution with two parameters for the Hankel transform and related integral operators”, Integral Transform. Spec. Funct., 28:1 (2016), 1–14  crossref  mathscinet  isi  scopus
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