Mathematical Methods in the Physical Sciences · Problem 5.23

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · parseval-theorem-symmetrized

Problem

Show that if (4.2) is written with the factor

1/\sqrt{2\pi}

multiplying each integral, then the corresponding form of Parseval's theorem (5.17) is

\int_{-\infty}^{\infty} |f(x)|^2\, dx = \int_{-\infty}^{\infty} |g(\alpha)|^2\, d\alpha.