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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
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Integral Equations with Difference Kernels on Finite Intervals - Second Edition, Revised and Extended (Paperback, 2nd revised and extended ed. 2015)
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Integral Equations with Difference Kernels on Finite Intervals - Second Edition, Revised and Extended (Paperback, 2nd revised and extended ed. 2015)
Series: Operator Theory: Advances and Applications, 84
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This book focuses on solving integral equations with difference
kernels on finite intervals. The corresponding problem on the
semiaxis was previously solved by N. Wiener-E. Hopf and by M.G.
Krein. The problem on finite intervals, though significantly more
difficult, may be solved using our method of operator identities.
This method is also actively employed in inverse spectral problems,
operator factorization and nonlinear integral equations.
Applications of the obtained results to optimal synthesis, light
scattering, diffraction, and hydrodynamics problems are discussed
in this book, which also describes how the theory of operators with
difference kernels is applied to stable processes and used to solve
the famous M. Kac problems on stable processes. In this second
edition these results are extensively generalized and include the
case of all Levy processes. We present the convolution expression
for the well-known Ito formula of the generator operator, a
convolution expression that has proven to be fruitful. Furthermore
we have added a new chapter on triangular representation, which is
closely connected with previous results and includes a new
important class of operators with non-trivial invariant subspaces.
Numerous formulations and proofs have now been improved, and the
bibliography has been updated to reflect more recent additions to
the body of literature.
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