Geodesic
On connection of one class of one-dimensional pseudodifferential operators with singular integral operators
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2009), pp. 8-15

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The paper discusses a homogeneous one-dimensional pseudodifferential equation with a symbol of the form $$A(x,\xi)=A_0(\xi)+\displaystyle\sum_{k=1}^N\tan\dfrac{\pi}{\alpha}\left(x-\lambda_k+i\dfrac{\alpha\beta}{2}\right)A_k(\xi) ~\ \ (x,\xi, ~\lambda_k\in \mathbb{R}, \alpha>0, ~-1\beta1, ~k=1,2,\dots,N),$$ where $A_k(\xi)~~ (k=0,1,\dots,N)$ are locally integrable functions from class of symbols of non-negative order $r$. The method of bringing the pseudodifferential equation to a system of onedimensional singular integral equations with Cauchy’s kernel is proposed.
Keywords: pseudodifferential operator, factorization of matrix-function. 
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     author = {V. V. Simonyan},
     title = {On connection of one class of one-dimensional pseudodifferential operators with singular integral operators},
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V. V. Simonyan. On connection of one class of one-dimensional pseudodifferential operators with singular integral operators. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2009), pp. 8-15. http://geodesic.mathdoc.fr/item/UZERU_2009_2_a1/