Determinants,finite-difference operators and boundary value problems |
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Authors: | Robin Forman |
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Affiliation: | 1. Department of Mathematics, Rice University, 77251, Houston, TX, USA
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Abstract: | We relate the determinants of differential and difference operators to the boundary values of solutions of the operators. Previous proofs of related results have involved considering one-parameter families of such operators, showing the desired quantities are equal up to a constant, and then calculating the constant. We take a more direct approach. For a fixed operator, we prove immediately that the two sides of our formulas are equal by using the following simple observation (Proposition 1.3):Let USU(n,C).Write U in block form
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