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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 1996 • Question 5

Question

Math 6210 • Real Analysis Fall 1996 • Question 5

Using the definitions of convolution and of Fourier transform show that, for \(f,g\in L^1(\mathbb R)\), \[ \widehat {(f*g)}(t)=\hat f(t)\hat g(t) \] for \(t\in \mathbb R\).

Raw LaTeX

Using the definitions of convolution and of Fourier transform show
that, for \(f,g\in L^1(\mathbb R)\),
\[
\widehat{(f*g)}(t)=\hat f(t)\hat g(t)
\]
for \(t\in\mathbb R\).

Topic Tags

Fourier Analysis and Convolution Lp Spaces and Sequence Spaces