The inversion theorem and Plancherel’s theorem in a Banach space
The inversion theorem and Plancherel’s theorem in a Banach space
U. HAUSSMANN l Introduction* Let G be a locally compact abelian group with Haar measure μ, and let X be a complex Banach space and C be the set of complex numbers.A classic theorem due to Plancherel ([8], [10]) states that the Fourier transform maps L X {G, C) Π …