Some new approaches to convolution equations

The following methods for studying and solving of integral and discrete convolution equations are presented, which have been developed recently by the authors.

1. The method of semi-inverse factorization. Applications to scalar and vector Wiener-Hopf equations.
2. Тwo -side continuation method for an equation on a finite interval.
3. Тhe method of averaging the kernel. Discretization and finite-diagonal reduction. Combination with Baxter-Hirschman type formulas.

 The results are compared with some known results obtained using the Wiener-Hopf method. Applications to problems of Mathematical physics are noted.