Integral Equations with Difference Kernels on Finite Intervals

1. An Invertible Operator with a Difference Kernel.-
1. Constructing the inverse operator.-
2. Existence conditions and the structure of the inverse operator.-
3. Equations with a special right-hand side.-
4. Operators with a difference kernel in the space Lp(0,?).-
5. The use of the Fourier transform.-
6. Toeplitz matrices.- 2. Equations of the first kind with a Difference Kernel.-
1. Equations of the first kind with a special right-hand side.-
2. Solutions of equations of the first kind.-
3. Generalized solutions.-
4. On the behavior of solutions.-
5. On one class of integro-differential equations.- 3. Examples and Applications.-
1. Integral equations with kernels of power type.-
2. Integral equations with logarithmic type kernels.-
3. Regularization.-
4. Fractional integrals of purely imaginary order.-
5. On a class of integral equations which are solvable in exact form.-
6. On certain problems of hydrodynamics.-
7. Equations on the contact theory of elasticity.-
8. The equation of radiation transfer.- 4. Eigensubspaces and Fourier transform.-
1. Classification of eigensubspaces.-
2. On the distribution of the roots of Fourier images.- 5. Operator Bezoutiant and Roots of Entire Functions.-
1. Definition and properties of the operator B.-
2. Operator T corresponding to a pair of entire functions.- 6. Operator Identities and Systems of Equations with W-difference Kernel.-
1. The principal notions of S-knot theory.-
2. Systems with W -difference kernels.-
3. Prandtl equation.- 7. Integral Equations in the Theory of Stable Processes.-
1. The deduction of the integro-differential equations.-
2. Solution of the Kac problems.-
3. Two-sided estimation of the smallest eigenvalue of the operator.- 8. Problems ofCommunication Theory.-
1. Problem of optimal prediction.-
2. Problem of diffraction on a strip.-
3. Extremal problems in the theory of synthesis of antennae.- Commentaries and Remarks.- References.