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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2017, Volume 2, Issue 1, Pages 30–45 (Mi chfmj43)  

This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

Solving of functional equations associated with the scalar product

V. A. Kyrov

Gorno-Altaisk State University, Gorno-Altaisk , Russia
Full-text PDF (718 kB) Citations (2)
References:
Abstract: The functional equations
$$\left[X\right]\frac{\partial \chi}{\partial \theta} + X_{n+1}(x^{n+1})\frac{\partial \chi}{\partial x^{n+1}} + X_{n+1}(y^{n+1})\frac{\partial \chi}{\partial y^{n+1}} = 0,$$
$$[X]\frac{\partial \sigma}{\partial \theta} + (X_{n+1}(x) - X_{n+1}(y))\frac{\partial \sigma}{\partial w} = 0,  [X]\frac{\partial \varkappa}{\partial \theta} + (X_{n+1}(x) + X_{n+1}(y))\frac{\partial \varkappa}{\partial z} = 0, $$ is solved in the paper. Here $[X] = \sum^{n}_{k=1}\bigl(\varepsilon_kx^kX_k(y) + \varepsilon_ky^kX_k(x))$, $x = (x^1,\ldots,x^n,x^{n+1})$, $\varepsilon_k=\pm1$, the equations are arising in the embedding problem of the space $\mathbb R^n$ with the inner product of the form $\theta = \varepsilon_1x^1y^1 + \cdots + \varepsilon_nx^ny^n$. In this problem, all kinds of functions $f = f(\theta,x^{n+ 1},y^{n+ 1}) $ are found that are two-point invariants of $n(n + 1)/2$-parametric group of transformations.
Keywords: functional equation, functional-differential equation, differential equation, scalar product.
Received: 25.12.2016
Revised: 28.02.2017
Bibliographic databases:
Document Type: Article
UDC: 517.965
Language: Russian
Citation: V. A. Kyrov, “Solving of functional equations associated with the scalar product”, Chelyab. Fiz.-Mat. Zh., 2:1 (2017), 30–45
Citation in format AMSBIB
\Bibitem{Kyr17}
\by V.~A.~Kyrov
\paper Solving of functional equations associated with the scalar product
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2017
\vol 2
\issue 1
\pages 30--45
\mathnet{http://mi.mathnet.ru/chfmj43}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3653289}
\elib{https://elibrary.ru/item.asp?id=29078325}
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  • https://www.mathnet.ru/eng/chfmj/v2/i1/p30
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Chelyabinskiy Fiziko-Matematicheskiy Zhurnal
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    Full-text PDF :106
    References:37
     
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