A mixed Parseval equation and the generalized Hankel transformations
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- by J. M. Méndez PDF
- Proc. Amer. Math. Soc. 102 (1988), 619-624 Request permission
Abstract:
Let ${T_1}$ and ${T_2}$ be two classical integral transforms whose inverse formulas coincide with themselves, satisfying the mixed Parseval equation \[ \int _0^\infty {f(x)g(x)dx = \int _0^\infty {{F_1}(y){G_2}(y)} \;dy,} \] where ${F_1}(y) = ({T_1}f)(y)$ and ${G_2}(y) = ({T_2}g)(y)$. We propose to define the generalized transformation ${T’_1}$ as the adjoint operator of ${T_2}$, and conversely. This procedure provides a new approach to extend the Hankel transform to certain spaces of distributions.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 619-624
- MSC: Primary 46F12; Secondary 44A05, 47B35
- DOI: https://doi.org/10.1090/S0002-9939-1988-0928991-5
- MathSciNet review: 928991