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Symbolic Computation Applied to the Study of the Kernel of a Singular Integral OperatorwithNon-Carleman Shift and Conjugation

Ana C. Conceição
Rui C. Marreiros
José C. Pereira
Journal / Anthology

Mathematics in Computer Science
Year: 2016
Volume: 10
Page range: 365-386

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 =  mj =0 a jU j , a, a j , j = 1,m, are continuous functions on the unit circle T, U is the shift operator and C is the operator of complex conjugation. We show how the symbolic computation capabilities of the computer algebra system Mathematica can be used to explore the dimension of the kernel of the operator K. The analytical algorithm [ADimKer-NonCarleman] is presented; several nontrivial examples are given.

*Applied Mathematics > Computer Science