Eigenfunction Expansions and Transformation Theory |
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Authors: | Manuel Gadella Fernando Gómez-Cubillo |
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Institution: | 1.Dpto. de Física Teórica, Facultad de Ciencias,Universidad de Valladolid,Valladolid,Spain;2.Dpto. de Análisis Matemático, Facultad de Ciencias,Universidad de Valladolid,Valladolid,Spain |
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Abstract: | Generalized eigenfunctions may be regarded as vectors of a basis in a particular direct integral of Hilbert spaces or as elements
of the antidual space Φ× in a convenient Gelfand triplet Φ⊆ℋ⊆Φ×. This work presents a fit treatment for computational purposes of transformations formulas relating different generalized
bases of eigenfunctions in both frameworks direct integrals and Gelfand triplets. Transformation formulas look like usual
in Physics literature, as limits of integral functionals but with well defined kernels. Several approaches are feasible. Vitali
approach is used. |
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Keywords: | |
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