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.