ON CONNECTION OF ONE CLASS OF ONE-DIMENSIONAL PSEUDODIFFERENTIAL OPERATORS WITH SINGULAR INTEGRAL OPERATORS
DOI:
https://doi.org/10.46991/PYSU:A/2009.43.2.008Keywords:
pseudodifferential operator, factorization of matrix-functionAbstract
The paper discusses a homogeneous one-dimensional pseudodifferential equation with a symbol of the form
$$A(x, \xi)=A_0(\xi)+\sum\limits_{k=1}^N th\frac{\pi}{\alpha}\left (x-\lambda_k+i\frac{\alpha\beta}{2}\right )A_k(\xi)$$
$$(x, \xi, \lambda \in \mathbb{R}, \alpha>0, -1<\beta<1, k=1,2,…,N ), $$
where $A_k(\xi) ( k=0,1,...,N)$ 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.
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Published
2009-06-26
How to Cite
Simonyan, V. V. (2009). ON CONNECTION OF ONE CLASS OF ONE-DIMENSIONAL PSEUDODIFFERENTIAL OPERATORS WITH SINGULAR INTEGRAL OPERATORS. Proceedings of the YSU A: Physical and Mathematical Sciences, 43(2 (219), 8–15. https://doi.org/10.46991/PYSU:A/2009.43.2.008
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Mathematics
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