Let D(1) denote the set of all first order linear differential operators L = p(x) D +
Question:
(a) Prove that D(1) is a vector space. Is it finitedimensional or infinite-dimensional?
(b) Prove that the commutator (7.15) of L, M ∈ D(1) is a first order differential operator [L, M] ∈ D(1) by writing out an explicit formula.
(c) Verify the Jacobi identity (7.16) for the first order differential operators L = D, M = x D + 1, and N = x2 D + 2x.
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a D 1 is a subspace of the vector space of all linear operato...View the full answer
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