# Groups, Special Functions and Rigged Hilbert Spaces

@article{Celeghini2019GroupsSF, title={Groups, Special Functions and Rigged Hilbert Spaces}, author={Enrico Celeghini and Manuel Gadella and Mariano A. del Olmo}, journal={Axioms}, year={2019}, volume={8}, pages={89} }

We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special functions serve as bases for infinite dimensional Hilbert spaces supporting linear unitary irreducible representations of a given Lie group. These representations are explicitly given by operators on the Hilbert space H and the generators of the Lie algebra are…

## 6 Citations

### Groups, Jacobi functions, and rigged Hilbert spaces

- MathematicsJournal of Mathematical Physics
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This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in…

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It is shown that an MBQC with CV-ﬂow approximates a unitary arbitrarily well in the inﬁnite-squeezing limit, addressing issues of convergence which are unavoidable in the on-the-fly setting of the measurement-based quantum computing setting.

### Zernike functions, rigged Hilbert spaces, and potential applications

- Mathematics, PhysicsJournal of Mathematical Physics
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We revise the symmetries of the Zernike polynomials that determine the Lie algebra su(1,1) + su(1,1). We show how they induce discrete as well continuous bases that coexist in the framework of rigged…

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