Solution of the Tricomi problem for the Lavrentiev-Batsadze equation by spectral analysis

In this work, the eigenvalues and corresponding eigenfunctions of the Tricomi-Neumann spectral problem for the Lavrentiev-Bitsadze operator are found. The found system of eigenfunctions is examined for completeness in the domains of ellipticity, hyperbolicity, and in general in the mixed domain. Solutions of the Tricomi-Neumann problems for equations of mixed type with the Lavrentiev-Bitsadze operator are constructed in the form of a sum of biorthogonal series for the eigenfunctions of the spectral problem.