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Solution of the Hadamard problem in the class of stepwise gauge-equivalent deformations of homogeneous differential operators with constant coefficients


Author: S. P. Khekalo
Translated by: the author
Original publication: Algebra i Analiz, tom 19 (2007), nomer 6.
Journal: St. Petersburg Math. J. 19 (2008), 1015-1028
MSC (2000): Primary 53A04; Secondary 52A40, 52A10
DOI: https://doi.org/10.1090/S1061-0022-08-01034-0
Published electronically: August 22, 2008
MathSciNet review: 2411965
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Abstract | References | Similar Articles | Additional Information

Abstract: In the paper, all nontrivial Huygens stepwise gauge-equivalent deformations for a priori Huygens homogeneous differential operators with constant coefficients are described explicitly. A condition is obtained under which an operator in the class of stepwise gauge-equivalent operators is Huygens, and new examples are given of iso-Huygens deformations of radial homogeneous differential operators of higher order.


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Additional Information

S. P. Khekalo
Affiliation: Kolomna State Pedagogical University, Russia
Email: fmf@kolomna.ru

DOI: https://doi.org/10.1090/S1061-0022-08-01034-0
Keywords: Hadamard problem, Huygens principle, homogeneous operators, deformations, Riesz kernels, gauge equivalence, stepwise gauge equivalence
Received by editor(s): September 21, 2007
Published electronically: August 22, 2008
Additional Notes: Supported by the president of RF (grant no. MK-2195.2007.1) and by RFBR (grant no. 07-01-00085).
Article copyright: © Copyright 2008 American Mathematical Society

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