Explore BrainMass

Explore BrainMass

    Eignevalues and Eigenvectors of the Fourier Transform

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Please see the attached file for the fully formatted problems.

    The Fourier transform, call it F, is a linear one-to-one operator from the space of square-integrable functions onto itself. (In fact, we also know that F is an "isometric" mapping, but we will not need this feature in this problem). Indeed,

    Note that here x and k are viewed as points on the common domain (?co, oo) of f and F.
    (a) Consider the linear operator P and its eigenvalue equation. What are the eigenvahies and the eigenfunctions of F2?
    (b) Identify the operator F4? What are its eigenvalues? (c) What are the eigenvalues of F?

    © BrainMass Inc. brainmass.com March 4, 2021, 5:54 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/eignevalues-and-eigenvectors-example-problem-17174

    Attachments

    Solution Summary

    Eignevalues and eigenvectors of the Fourier transform are investigated. The solution is detailed and well presented.

    $2.49

    ADVERTISEMENT