Spectral theory of a pencil of skew-symmetric differential operators of third order on S1
β Scribed by I. M. Gel'fand; I. S. Zakharevich
- Publisher
- Springer US
- Year
- 1989
- Tongue
- English
- Weight
- 779 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0016-2663
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## Abstract We investigate the spectral theory of a general third order formally symmetric differential expression of the form acting in the Hilbert space βοΈ^2^~__w__~ (__a__ ,β). A KummerβLiouville transformation is introduced which produces a differential operator unitarily equivalent to __L__
Let M be a smooth manifold endowed with a flat conformal structure and F Ξ» (M) the space of densities of degree Ξ» on M. We study the space D 3 Ξ»,Β΅ (M) of third-order differential operators from F Ξ» (M) to F Β΅ (M) as a module over the conformal Lie algebra o(p + 1, q + 1). We prove that D 3 Ξ»,Β΅ (M) i