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Algebra i Analiz, 2007, Volume 19, Issue 6, Pages 200–219 (Mi aa153)  

Research Papers

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

S. P. Khekalo

Kolomna State Pedagogical Institute

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.

Keywords: Hadamard problem, Huygens principle, homogeneous operators, deformations, Riesz kernels, gauge equivalence, stepwise gauge equivalence.

Full text: PDF file (313 kB)
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English version:
St. Petersburg Mathematical Journal, 2008, 19:6, 1015–1028

Bibliographic databases:

MSC: Primary 53A04; Secondary 52A40, 52A10
Received: 21.09.2007

Citation: S. P. Khekalo, “Solution of the Hadamard problem in the class of stepwise gauge-equivalent deformations of homogeneous differential operators with constant coefficients”, Algebra i Analiz, 19:6 (2007), 200–219; St. Petersburg Math. J., 19:6 (2008), 1015–1028

Citation in format AMSBIB
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\paper Solution of the Hadamard problem in the class of stepwise gauge-equivalent deformations of homogeneous differential operators with constant coefficients
\jour Algebra i Analiz
\yr 2007
\vol 19
\issue 6
\pages 200--219
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\zmath{https://zbmath.org/?q=an:1206.35162}
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\transl
\jour St. Petersburg Math. J.
\yr 2008
\vol 19
\issue 6
\pages 1015--1028
\crossref{https://doi.org/10.1090/S1061-0022-08-01034-0}
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