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Hilbert spaces of generalized functions extending L2, (I)

Published online by Cambridge University Press:  09 April 2009

John Boris Miller
John Boris Miller
Affiliation:
Australian National University, Canberra, A.C.T.
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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).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 1 , Issue 3 , August 1960 , pp. 281 - 298
Copyright
Copyright © Australian Mathematical Society 1960

References

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