Eignevalues and Eigenvectors of the Fourier Transform
Not what you're looking for?
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?
Purchase this Solution
Solution Summary
Eignevalues and eigenvectors of the Fourier transform are investigated. The solution is detailed and well presented.
Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Probability Quiz
Some questions on probability
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.