A Paley–Wiener theorem for some eigenfunction expansions

S. Thangavelu 1
  • 1 Department of Mathematics, Indian Institute of Science, Bangalore-560 012, India.


We prove a general version of Paley–Wiener theorem characterising functions with finite Fourier expansions. The result covers Fourier series on compact symmetric spaces, Hermite and special Hermite expansions as particular cases. Gutzmer's formula plays an important role in the formulation and proof of the theorem.

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