F. N. Garif'yanov, “On a Certain Difference Equation and Its Application to the Moment Problem”, Mat. Zametki, 73:6 (2003), 821–826; Math. Notes, 73:6 (2003), 777

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Matematicheskie Zametki, 2003, Volume 73, Issue 6, Pages 821–826
DOI: https://doi.org/10.4213/mzm229 (Mi mzm229)

This article is cited in 5 scientific papers (total in 5 papers)

On a Certain Difference Equation and Its Application to the Moment Problem

F. N. Garif'yanov

Kazan State Agricultural Academy

Full-text PDF (169 kB) Citations (5)

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DOI: https://doi.org/10.4213/mzm229

Abstract: We study the difference equation

\sum_{m_{1}, m_{2}} Ω [σ_{m_{1}, m_{2}} (z)] = g (z), z \in D,

$\sum_{m_1,m_2}\Omega[\sigma_{m_1,m_2}(z)]=g(z), \qquad z\in D,$
where

D

$D$ is the unit square,

g (z) \in A (D)

$g(z)\in A(D)$ ,

σ_{m_{1}, m_{2}} (z) = z + m_{1} i + m_{2}

$\sigma_{m_1,m_2}(z)=z+m_1i+m_2$ ,

| m_{1} | + | m_{2} | = 2

$|m_1|+|m_2|=2$ , and

Ω (z) \in A (c D)

$\Omega(z)\in A(cD)$ is an unknown function.

Received: 18.05.2000

English version:
Mathematical Notes, 2003, Volume 73, Issue 6, Pages 777–782
DOI: https://doi.org/10.1023/A:1024041511679

Bibliographic databases:

UDC: 517.96

Language: Russian

Citation: F. N. Garif'yanov, “On a Certain Difference Equation and Its Application to the Moment Problem”, Mat. Zametki, 73:6 (2003), 821–826; Math. Notes, 73:6 (2003), 777–782

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm229

https://doi.org/10.4213/mzm229

https://www.mathnet.ru/eng/mzm/v73/i6/p821

This publication is cited in the following 5 articles:

F. N. Garif'yanov, “Polyelement functional equations related to the Carleman kernel and their applications”, Russian Math. (Iz. VUZ), 66:11 (2022), 18–32
F. N. Garif'yanov, E. V. Strezhneva, “On a Carleman problem in the case of a doubly periodic group”, Probl. anal. Issues Anal., 11(29):3 (2022), 45–55
Garif'yanov F.N. Strezhneva E.V., “On a Difference Equation Generated By Two “Close” Squares”, Lobachevskii J. Math., 40:1, SI (2019), 55–59
F. N. Garif'yanov, E. V. Strezhneva, “Difference equation for functions analytical outside two squares”, Russian Math. (Iz. VUZ), 62:6 (2018), 1–5
F. N. Garif'yanov, S. A. Modina, “The Carleman kernel and its applications”, Siberian Math. J., 53:6 (2012), 1011–1020

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	185
References:	45
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