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Multidimensional Baker-Akhiezer functions and Huygens' Principle
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A notion of rational Baker-Akhiezer (BA) function related to a configuration of hyperplanes in C^n is introduced. It is proved that BA function exists only for very special configurations (locus configurations), which satisfy certain overdetermined algebraic system. The BA functions satisfy some algebraically integrable Schrodinger equations, so any locus configuration determines such an equation. Some results towards the classification of all locus configurations are presented. This theory is applied to the famous Hadamard's problem of description of all hyperbolic equations satisfying Huygens' Principle. We show that in a certain class all such equations are related to locus configurations and the corresponding fundamental solutions can be constructed explicitly from the BA functions.
Forward citations
Cited by 2 Pith papers
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A basic triad in Macdonald theory
At t=q^{-m}, the Noumi-Shiraishi series reproduces the Baker-Akhiezer function, completing a triad with the Macdonald polynomials.
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Chalykh's Baker-Akhiezer functions as eigenfunctions of the integer-ray integrable systems
In explicit small cases, twisted Baker-Akhiezer functions satisfy the defining linear equations and are eigenfunctions of the integer-ray DIM Hamiltonians.
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