Integral Equations with Difference Kernels on Finite Intervals - Sakhnovich, Lev A.

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Résumé :
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Sommaire:
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 of Communication 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.