|Title||Reduction of spectral problem of Cauchy-Riemann operator with homogeneous boundary conditions to an integral equation|
|Keywords||Differential operation of the Cauchy-Riemann, elliptic operators|
In this paper the problem on the eigenvalues of the Cauchy-Riemann operator with homogeneous boundary conditions is reduced to an integral equation.
|Title||MIXED PROBLEM FOR A DIFFERENTIAL EQUATION WITH INVOLUTION UNDER BOUNDARY CONDITIONS OF GENERAL FORM|
|Keywords||mixed problem, involution, the Fourier method, the Riesz basis, biorthogonal decomposition, classical solution|
To solve the mixed problem for a partial differential equation with involution and a symmetric potential there was found an explicit analytical representation by the Fourier method. The problem was considered under general boundary conditions with constant coefficients by a space variable. At the same we used the methods for avoiding the termwise differentiation of a functional series and applying the minimal conditions on initial data of the problem.