Integral Equations

Classification of Kernels (IEL4)

Posted by jessepfrancis on

Kernels are classified based on the following criteria:

  1. Separable/Degenerate: K(s,t) = \sum a_i(s)b_i(t)
  2. Symmetric or Hermitian: K(s,t) = K^*(t,s), where * denotes the conjugate
  3. Convolution Type: K(s,t) = K(s-t)

Note that a kernel may be of two types at the same time.

For example, K(s,t)=s-t is of both separable and of convolution type. It is not symmetric as K(t,s)\ne K(s,t). You will find more examples in the quiz (link).

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Published by jessepfrancis

Christian. Artist. Mathematician. Programmer. Teacher. Visit https://mathematicos.in/aboutjesse/ for my full profile.

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