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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2015 • Question 9

Question

Math 6420 • PDE Fall 2015 • Question 9

  1. Calculate the Fourier transform of a Gaussian \(f(x)=e^{-x^2}\) (\(x\in \mathbb {R}\)).
  2. Is it possible that a function \(f(x)\) (\(x\in \mathbb {R}\)) and its Fourier transform \(F(\mu )\) (\(\mu \in \mathbb {R}\)) both have finite support?

Raw LaTeX

\begin{enumerate}
\item[(a)] Calculate the Fourier transform of a Gaussian \(f(x)=e^{-x^2}\) (\(x\in\mathbb{R}\)).

\item[(b)] Is it possible that a function \(f(x)\) (\(x\in\mathbb{R}\)) and its Fourier
transform \(F(\mu)\) (\(\mu\in\mathbb{R}\)) both have finite support?
\end{enumerate}

Topic Tags

Fourier Transform and Sampling Theory Gaussian Elimination and Pivoting Linear Programming and Optimization