In this paper we give another characterization of the strictly nilpotent elements in the Weyl algebra, which (apart from the polynomials) turn out to be all bispectral operators with polynomial coefficients. This also allows to reformulate in terms of bispectral operators the famous conjecture, that
Weyl pair, current algebra and shift operator
β Scribed by Zhan-Ning Hu
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 339 KB
- Volume
- 197
- Category
- Article
- ISSN
- 0375-9601
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π SIMILAR VOLUMES
Let M(clR") be a smooth compact manifold. Recall (see, for instance, [3, 61) that a bounded linear operator S in L,(M) is called an abstract singular operator if the following conditions (axioms) hold: 1. the operator S2 -I is compact (and the operators S f Z are noncompact); 2. the operator S\* -S
In the present paper we consider the shift operator S on the Wiener algebra W (D) of analytic functions on the unit disc D of the complex plane C. A complex number Ξ» is called an extended eigenvalue of S if there exists a nonzero operator A satisfying the equation AS = Ξ»SA. We prove that the set of