Some integral equations with 'nonrational' kernels | IEEE Journals & Magazine | IEEE Xplore

Some integral equations with 'nonrational' kernels


Abstract:

Fredholm integral equations of the first and second kind arise in many problems in statistical communication theory. However, almost all cases in which solutions are know...Show More

Abstract:

Fredholm integral equations of the first and second kind arise in many problems in statistical communication theory. However, almost all cases in which solutions are known, for equations over finite intervals, involve covariance kernels with rational Fourier transforms. We present solutions for two classes of "non-rational" kernels--triangular kernels of the formR(t) = \max [0, 1 - |t|]and Gauss-Markov kernels of the formR(t, s) = f(t)g(s), t \leq s, R(t, s) = f(s)g(t), s \leq t. We also treat kernels that are combinations of the two types.
Published in: IEEE Transactions on Information Theory ( Volume: 12, Issue: 4, October 1966)
Page(s): 442 - 447
Date of Publication: 06 January 2003

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