Multidimensional Baker-Akhiezer functions and Huygens' principle

A notion of The rational Baker-Akhiezer (BA) function related to a configuration of hyperplanes in Cn is introduced. It is proved that the BA function exists only for very special configurations (locus configurations), which satisfy a certain overdetermined algebraic system, The BA functions satisfy...

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Main Authors: O.A. Chalykh, Mikhail V. Feigin, Alexander Veselov
Format: Default Preprint
Published: 1999
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Online Access:https://hdl.handle.net/2134/828
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spelling rr-article-93789111999-01-01T00:00:00Z Multidimensional Baker-Akhiezer functions and Huygens' principle O.A. Chalykh (7160021) Mikhail V. Feigin (7158413) Alexander Veselov (1259028) Other mathematical sciences not elsewhere classified Foundations of quantum mechanics untagged Quantum Mechanics Mathematical Sciences not elsewhere classified A notion of The rational Baker-Akhiezer (BA) function related to a configuration of hyperplanes in Cn is introduced. It is proved that the BA function exists only for very special configurations (locus configurations), which satisfy a 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 problem of description of all hyperbolic equations satisfying Huygens' Principle. We show that in a certain class all such equations an related to locus configurations and the corresponding fundamental solutions can be constructed explicitly from the BA functions. 1999-01-01T00:00:00Z Text Preprint 2134/828 https://figshare.com/articles/preprint/Multidimensional_Baker-Akhiezer_functions_and_Huygens_principle/9378911 CC BY-NC-ND 4.0
institution Loughborough University
collection Figshare
topic Other mathematical sciences not elsewhere classified
Foundations of quantum mechanics
untagged
Quantum Mechanics
Mathematical Sciences not elsewhere classified
spellingShingle Other mathematical sciences not elsewhere classified
Foundations of quantum mechanics
untagged
Quantum Mechanics
Mathematical Sciences not elsewhere classified
O.A. Chalykh
Mikhail V. Feigin
Alexander Veselov
Multidimensional Baker-Akhiezer functions and Huygens' principle
description A notion of The rational Baker-Akhiezer (BA) function related to a configuration of hyperplanes in Cn is introduced. It is proved that the BA function exists only for very special configurations (locus configurations), which satisfy a 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 problem of description of all hyperbolic equations satisfying Huygens' Principle. We show that in a certain class all such equations an related to locus configurations and the corresponding fundamental solutions can be constructed explicitly from the BA functions.
format Default
Preprint
author O.A. Chalykh
Mikhail V. Feigin
Alexander Veselov
author_facet O.A. Chalykh
Mikhail V. Feigin
Alexander Veselov
author_sort O.A. Chalykh (7160021)
title Multidimensional Baker-Akhiezer functions and Huygens' principle
title_short Multidimensional Baker-Akhiezer functions and Huygens' principle
title_full Multidimensional Baker-Akhiezer functions and Huygens' principle
title_fullStr Multidimensional Baker-Akhiezer functions and Huygens' principle
title_full_unstemmed Multidimensional Baker-Akhiezer functions and Huygens' principle
title_sort multidimensional baker-akhiezer functions and huygens' principle
publishDate 1999
url https://hdl.handle.net/2134/828
_version_ 1800279214203600896