A rigged Hilbert space of Hardy‐class functions: Applications to resonances

The explicit construction of a dense subspace Φ of square integrable functions on the positive half of the real line is given. This space Φ has the properties that: (1) it is endowed with a metrizable nuclear topology, (2) it is stable under multiplication by x, and (3) the functions in Φ have suitable analytical continuation to a half plane. The space Φ* of functions which are conjugate to elements of Φ is also considered. Then the triplets Φ⊆ L2 (0,∞)⊆Φ′ and Φ*⊆ L2 (0,∞)⊆Φ*′ are used to give a description of resonances.

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