An integral formula for L 2-eigenfunctions of a fourth-order Bessel-type differential operator

@article{Kobayashi2011AnIF,
  title={An integral formula for L 2-eigenfunctions of a fourth-order Bessel-type differential operator},
  author={Toshiyuki Kobayashi and Jan M{\"o}llers},
  journal={Integral Transforms and Special Functions},
  year={2011},
  volume={22},
  pages={521 - 531}
}
We find an explicit integral formula for the eigenfunctions of a fourth-order differential operator against the kernel involving two Bessel functions. Our formula establishes the relation between K-types in two different realizations of the minimal representation of the indefinite orthogonal group, namely the L 2-model and the conformal model. 

Minimal representations via Bessel operators

We construct an L^2-model of "very small" irreducible unitary representations of simple Lie groups G which, up to finite covering, occur as conformal groups Co(V) of simple Jordan algebras V. If $V$

Special Functions in Minimal Representations

Minimal representations of a real reductive group G are the `smallest' irreducible unitary representations of G. We discuss special functions that arise in the analysis of L^2-model of minimal

Varna Lecture on L 2 -Analysis of Minimal Representations

Minimal representations of a real reductive group G are the ‘smallest’ irreducible unitary representations of G. The author suggests a program of global analysis built on minimal representations from

References

SHOWING 1-10 OF 15 REFERENCES

Special functions associated with a certain fourth-order differential equation

We develop a theory of “special functions” associated with a certain fourth-order differential operator $\mathcal{D}_{\mu,\nu}$ on ℝ depending on two parameters μ,ν. For integers μ,ν≥−1 with μ+ν∈2ℕ0,

Orthogonal polynomials associated to a certain fourth order differential equation

We introduce orthogonal polynomials $M_{j}^{\mu,\ell}(x)$ as eigenfunctions of a certain self-adjoint fourth order differential operator depending on two parameters μ∈ℂ and ℓ∈ℕ0.These polynomials

Integral formula of the unitary inversion operator for the minimal representation of O(p,q)

The indefinite orthogonal group G = O(p,q) has a distinguished infinite dimen- sional unitary representation …, called the minimal representation for p+q even and greater than 6. The Schrodinger

The Schrödinger model for the minimal representation of the indefinite orthogonal group (

The indenite orthogonal group G = O(p;q) has a distinguished innite dimensional irreducible unitary representation for p +q even and greater than 4, which is the \smallest" in the sense that the

Table of Integrals, Series, and Products

Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of Special

The Schrödinger model for the minimal representation of the indefinite orthogonal group O(p, q)

The authors introduce a generalization of the Fourier transform, denoted by $\mathcal{F}_C$, on the isotropic cone $C$ associated to an indefinite quadratic form of signature $(n_1,n_2)$ on

A Table of Integrals

Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + b dx = 1 a ln |ax + b| (4) Integrals of Rational Functions 1 (x + a) 2 dx = −