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On the spectral theory of multiparameter difference equations of second order
G. Sh. Guseinov
Abstract:
Let
\begin{gather*}
a_{n_r-1,r}y_{n_r-1,r}+b_{n_r,r}y_{n_r,r}+a_{n_r,r}y_{n_r+1,r}=
\biggl(\sum_{s=1}^k\lambda_s c_{n_r,r,s}\biggr)y_{n_r,r},\\
r=1,\dots,k,
\end{gather*}
be a system of
$k$ second-order difference equations (with real coefficients) containing
$k$ spectral parameters
$\lambda_1,\dots,\lambda_k$. The existence of spectral measures is established in the cases when
$n_1,\dots,n_k$ run through the integer points of the semiaxis and of the whole axis, the properties of the spectral measures are studied, and with their help formulas are written out for expansions in eigenvectors of this system. The case of periodic coefficients is investigated in greater detail.
Bibliography: 14 titles.
UDC:
517.984.46
MSC: Primary
39A10,
39A12; Secondary
39A11 Received: 22.04.1985
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