Analysis as a Life by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9783030026509
Publisher: Springer International Publishing

Let

(4.9)

and the matrix Riemann-Hilbert problem (4.2) is equivalently changed to

(4.10)

Clearly, the solutions of two independent matrix Riemann-Hilbert problems (4.2) and (4.10) are connected by the relation (4.9). We need the Cauchy-type integral operator

(4.11)

Next, we also have the following result, which describes the equivalent relation between the matrix Riemann-Hilbert problem (4.10) and the system of singular integral equations [16, 19, 20].

Lemma 4.2

If Δ is the solution of the matrix Riemann-Hilbert problem (4.10) , then the negative boundary-value Δ − solves the system of singular integral equations

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