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- W2888402566 abstract "On the vector Lebesgue space on the unit circle ({L}^{n}_{p} ({p} in (1, infty), {n} in mathbb{N}) we consider singular integral operators with a Carleman backward shift of linear fractional type, of the form ({T}_{A,B} = {AP}_{+} + {BP}_{-}) with A = aI + bU, B = cI + dU, where ({a, b, c, d} in {L}^{n times n}, {P}_{pm} = frac{1}{2}({I} {pm} {S})) are the Cauchy projectors in ({L}^{n}_{p}) defined componentwise, and U is an involutory shift operator associated with the given Carleman backward shift also defined componentwise. By generalization to the vector case (n > 1) of the previously obtained results for the scalar case (n = 1), it is shown that whenever a certain 2n × 2n matrix function, associated with the original singular integral operator, admits a bounded factorization in ({L}^{2n}_{p}) the Fredholm characteristics of the paired operator TA,B can be obtained in terms of that factorization, in particular the dimensions of the kernel and of the cokernel." @default.
- W2888402566 created "2018-08-31" @default.
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- W2888402566 date "2018-01-01" @default.
- W2888402566 modified "2023-09-23" @default.
- W2888402566 title "Factorization of Singular Integral Operators with a Carleman Backward Shift: The Vector Case" @default.
- W2888402566 doi "https://doi.org/10.1007/978-3-319-72449-2_12" @default.
- W2888402566 hasPublicationYear "2018" @default.
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