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Question about singular integral eq.

  1. Nov 24, 2013 #1
    Hi,
    I've questions about the Fredholm integral equation :
    1. Is an following eq.
    [itex]a(x)y(x) + \int^{∞}_{-∞}\frac{\sin(x-y)}{x-y}dy = f(x)[/itex]
    be defined as singular integral equation, if it is how can i get the solution?
    2. What is the definition of singular kernel and is the kernel in (1)?

    please help me or give me some suggestions/links to materials about these.

    Thank you.
     
  2. jcsd
  3. Nov 24, 2013 #2

    mathman

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    I suggest you look carefully at your post. The integral is constant (not dependent on x). I believe you need some function of y under the integral sign.
     
  4. Nov 24, 2013 #3
    Sorry, there are flaws in the above eq. It should be
    [itex]a(x)y(x) + \int^{∞}_{-∞}\frac{\sin(k(x-t))}{π(x-t)}y(t)dt = f(x)[/itex]
    where a(x) and f(x) are known functions, and y(x) is unknown function.
     
  5. Nov 24, 2013 #4
    Thanks you very much for that remark. In future, I will do it more carefully.
     
  6. Nov 25, 2013 #5

    mathman

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    It is called singular because the absolute value of the kernel is not integrable. Solving Fredholm equations is a major branch of analysis - there is no simple answer.
     
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