Author | Sakhnovich, Lev A. author |
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Title | Integral Equations with Difference Kernels on Finite Intervals [electronic resource] / by Lev A. Sakhnovich |
Imprint | Basel : Birkhรคuser Basel, 1996 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8986-5 |
Descript | 184 p. online resource |
1. An Invertible Operator with a Difference Kernel -- ยง1. Constructing the inverse operator -- ยง2. Existence conditions and the structure of the inverse operator -- ยง3. Equations with a special right-hand side -- ยง4. Operators with a difference kernel in the space Lp(0,?) -- ยง5. The use of the Fourier transform -- ยง6. Toeplitz matrices -- 2. Equations of the first kind with a Difference Kernel -- ยง1. Equations of the first kind with a special right-hand side -- ยง2. Solutions of equations of the first kind -- ยง3. Generalized solutions -- ยง4. On the behavior of solutions -- ยง5. On one class of integro-differential equations -- 3. Examples and Applications -- ยง1. Integral equations with kernels of power type -- ยง2. Integral equations with logarithmic type kernels -- ยง3. Regularization -- ยง4. Fractional integrals of purely imaginary order -- ยง5. On a class of integral equations which are solvable in exact form -- ยง6. On certain problems of hydrodynamics -- ยง7. Equations on the contact theory of elasticity -- ยง8. The equation of radiation transfer -- 4. Eigensubspaces and Fourier transform -- ยง1. Classification of eigensubspaces -- ยง2. On the distribution of the roots of Fourier images -- 5. Operator Bezoutiant and Roots of Entire Functions -- ยง1. Definition and properties of the operator B -- ยง2. Operator T corresponding to a pair of entire functions -- 6. Operator Identities and Systems of Equations with W-difference Kernel -- ยง1. The principal notions of S-knot theory -- ยง2. Systems with W -difference kernels -- ยง3. Prandtl equation -- 7. Integral Equations in the Theory of Stable Processes -- ยง1. The deduction of the integro-differential equations -- ยง2. Solution of the Kac problems -- ยง3. Two-sided estimation of the smallest eigenvalue of the operator -- 8. Problems of Communication Theory -- ยง1. Problem of optimal prediction -- ยง2. Problem of diffraction on a strip -- ยง3. Extremal problems in the theory of synthesis of antennae -- Commentaries and Remarks -- References