Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2004 • Question 5

Question

Math 6210 • Real Analysis 2004 • Question 5

Let \(f,g\in L^1(\mathbb R)\). Let \(A=f^{-1}(\mathbb C-\{0\})\) and \(B=g^{-1}(\mathbb C-\{0\})\). Show that \[ (f*g)^{-1}(\mathbb C-\{0\})\subset A+B \] where \(A+B=\{x+y:x\in A,y\in B\}\).

Raw LaTeX

Let \(f,g\in L^1(\mathbb R)\). Let
\(A=f^{-1}(\mathbb C-\{0\})\) and \(B=g^{-1}(\mathbb C-\{0\})\). Show that
\[
(f*g)^{-1}(\mathbb C-\{0\})\subset A+B
\]
where \(A+B=\{x+y:x\in A,y\in B\}\).

Topic Tags

Lp Spaces and Sequence Spaces