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Singularities of Solutions of Singular Integral Equations
Ukrainian Mathematical Journal, 2002This paper deals with a singular integral equation \[ Sq+Tq=f,\tag{1} \] where \(q(x)\) is an unknown function, \[ Sq(x):=aq(x)+\frac{1}{\pi }\text{v.p.} \int_{-1}^{1} \frac{q(\tau)}{\tau -x} d\tau,\;Tq(x):=\int_{-1}^{1}K(x,\tau)q(\tau) d\tau. \] It is assumed that the functions \(f\) and \(K\) smoothly depend on additional parameters.
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Mathematics of the USSR-Izvestiya, 1986In a space \(C^ n\) an integrable system of differential Pfaff equations of the form \(df=\omega f\) is considered, where f is an unknown p- dimensional vector of complex-valued functions, \(\omega =\sum^{m}_{i=1}A_ i\frac{dL_ i}{L_ i}\) is a matrix differential form, \(A_ i\) are constant commutative complex \(p\times p\)-matrices. It is supposed that
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