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AuthorSakhnovich, Lev A. author
TitleIntegral Equations with Difference Kernels on Finite Intervals [electronic resource] / by Lev A. Sakhnovich
ImprintBasel : Birkhรคuser Basel, 1996
Connect tohttp://dx.doi.org/10.1007/978-3-0348-8986-5
Descript 184 p. online resource

SUMMARY

Optimal synthesis, light scattering, and diffraction on a ribbon are just some of the applied problems for which integral equations with difference kernels are employed. The same equations are also met in important mathematical problems such as inverse spectral problems, nonlinear integral equations, and factorization of operators. On the basis of the operator identity method, the theory of integral operators with difference kernels is developed here, and the connection with many applied and theoretical problems is studied. A number of important examples are analyzed


CONTENT

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


Mathematics Mathematical analysis Analysis (Mathematics) Mathematics Analysis



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