Multidimensional BakerAkhiezer functions and Huygens' principle
A notion of The rational BakerAkhiezer (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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1999

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rrarticle937891119990101T00:00:00Z Multidimensional BakerAkhiezer 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 BakerAkhiezer (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. 19990101T00:00:00Z Text Preprint 2134/828 https://figshare.com/articles/preprint/Multidimensional_BakerAkhiezer_functions_and_Huygens_principle/9378911 CC BYNCND 4.0 
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Other mathematical sciences not elsewhere classified Foundations of quantum mechanics untagged Quantum Mechanics Mathematical Sciences not elsewhere classified 
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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 BakerAkhiezer functions and Huygens' principle 
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A notion of The rational BakerAkhiezer (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. 
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Default Preprint 
author 
O.A. Chalykh Mikhail V. Feigin Alexander Veselov 
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O.A. Chalykh Mikhail V. Feigin Alexander Veselov 
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O.A. Chalykh (7160021) 
title 
Multidimensional BakerAkhiezer functions and Huygens' principle 
title_short 
Multidimensional BakerAkhiezer functions and Huygens' principle 
title_full 
Multidimensional BakerAkhiezer functions and Huygens' principle 
title_fullStr 
Multidimensional BakerAkhiezer functions and Huygens' principle 
title_full_unstemmed 
Multidimensional BakerAkhiezer functions and Huygens' principle 
title_sort 
multidimensional bakerakhiezer functions and huygens' principle 
publishDate 
1999 
url 
https://hdl.handle.net/2134/828 
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1800279214203600896 