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Mat. Sb. (N.S.), 1987, Volume 132(174), Number 2, Pages 167–181 (Mi msb1771)  

Introduction to the theory of $(\nu_1,…,\nu_{r-1})$-transforms

M. I. Klyuchantsev


Abstract: The transforms
\begin{gather*} \varphi_\nu(x)=\int_0^\infty\dotsi\int_0^\infty f(x\prod t_i)e^{-\sum{t_i^r}}\prod t _i^{r{\nu_i}+r-1} dt_i,
f(x)=(\frac r{2\pi i})^{r-1}\int_{-\infty}^{(0+)}\dotsi\int_{-\infty}^{(0+)}\varphi_\nu(x\prod t_i^{-\frac1r})e^{\sum{t_i}}\prod t_i^{{-\nu_i}-1} dt_i \end{gather*}
are introduced for an integer $r\geqslant2$ and a given vector $\nu=(\nu_1,…,\nu_{r-1})$. Their duality is substantiated, applications of the differentiation operations are studied, and other properties of $\nu$-transforms are established. A number of examples are given to illustrate the method of $\nu$-transforms for solving some classes of differential equations and boundary value problems for partial differential equations.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Sbornik, 1988, 60:1, 163–176

Bibliographic databases:

UDC: 517.444
MSC: Primary 44A15; Secondary 34A05, 35A22
Received: 10.10.1985 and 31.07.1986

Citation: M. I. Klyuchantsev, “Introduction to the theory of $(\nu_1,…,\nu_{r-1})$-transforms”, Mat. Sb. (N.S.), 132(174):2 (1987), 167–181; Math. USSR-Sb., 60:1 (1988), 163–176

Citation in format AMSBIB
\Bibitem{Kly87}
\by M.~I.~Klyuchantsev
\paper Introduction to the theory of $(\nu_1,\dots,\nu_{r-1})$-transforms
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 132(174)
\issue 2
\pages 167--181
\mathnet{http://mi.mathnet.ru/msb1771}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=882832}
\zmath{https://zbmath.org/?q=an:0658.44006}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 60
\issue 1
\pages 163--176
\crossref{https://doi.org/10.1070/SM1988v060n01ABEH003161}


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