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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2018 • Question 9

Question

Math 6420 • PDE Fall 2018 • Question 9

\(F(\omega )\) is the Fourier transform of \(f(x)\) (which is continuous and not identical zero), \(x\) and \(\omega \) are real variables. Explain why it is impossible that both functions \(f(x)\) and \(F(\omega )\) have finite support.

Raw LaTeX

\(F(\omega)\) is the Fourier transform of \(f(x)\) (which is continuous and not identical
zero), \(x\) and \(\omega\) are real variables. Explain why it is impossible that both
functions \(f(x)\) and \(F(\omega)\) have finite support.

Topic Tags

Fourier Transform and Sampling Theory Linear Programming and Optimization Point, Continuous, and Residual Spectrum Variable-Coefficient Diffusion Problems