Home / Archives / Vol. 43 No. 2 (219) (2009) / Mathematics ON CONNECTION OF ONE CLASS OF ONE-DIMENSIONAL PSEUDODIFFERENTIAL OPERATORS WITH SINGULAR INTEGRAL OPERATORS

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Home / Archives / Vol. 43 No. 2 (219) (2009) / Mathematics ON CONNECTION OF ONE CLASS OF ONE-DIMENSIONAL PSEUDODIFFERENTIAL OPERATORS WITH SINGULAR INTEGRAL OPERATORS V.V. Simonyan

The paper discusses a homogeneous one-dimensional pseudodifferential equation with a symbol of the form

A(x,ξ)=A0(ξ)+∑k=1Nthπα(x−λk+iαβ2)Ak(ξ)

(x,ξ,λ∈R,α>0,−1<β<1,k=1,2,…,N),

where  Ak(ξ)(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.

DOI: 10.46991/PYSUA.2009.43.2.008 Physical and Mathematical Sciences, 43(2 (219) 8-15

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Keywords

pseudodifferential operator, factorization of matrix-function

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