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Hilbert spaces of generalized functions extending L2, (I)
Published online by Cambridge University Press: 09 April 2009
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By using certain fractional integrals and derivatives it is possible to construct a continuum of Hilbert spaces within the space L2 (0, ∞); these are the spaces gλ of functions f(x) for which 1xλf(λ)(x) є L2(0, ∞), and they exhibit invariance properties under generalized Fourier transformations. They are described in (6) and (7).
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- Copyright © Australian Mathematical Society 1960
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