Summation Method for Fourier Series Associated with a Mixed Problem for the Inhomogeneous Telegraph Equation

A summation method for Fourier series associated with a generalized mixed problem for the telegraph equation in a semi-infinite strip is proposed. The concept of the regularity of a summation method is introduced. It is shown that the generalized sum produced by this method can be used as a solution of the generalized mixed problem. Here, the generalized sum is specified by an exponentially converging function series. In the case of smooth initial data, this series gives a strong solution of the original pro-blem.