On the Kernel of a Singular Integral Operator with Non–carleman Shift and Conjugation
نویسندگان
چکیده
On the Hilbert space ̃L2(T) the singular integral operator with non-Carleman shift and conjugation K = P+ + (aI + AC)P− is considered, where P± are the Cauchy projectors, A = m ∑ j=0 ajU j , a,aj , j = 1,m , are continuous functions on the unit circle T , U is the shift operator and C is the operator of complex conjugation. Some estimates for the dimension of the kernel of the operator K are obtained. Mathematics subject classification (2010): Primary 47G10, 47A68; Secondary 45P05, 68W30.
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