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Eigenfunctions of the Gellerstedt problem with an inclined-type change line

ABSTRACT The Gellerstedt problem is considered for the elliptic–hyperbolic equation with a spectral parameter. There are two inclined-type change lines which form different arbitrary angles and with the x-axis. The eigenfunctions of this problem are constructed and the corresponding eigenvalues are found. The system of these eigenfunctions is proved to form a Riesz basis in the elliptic domain.