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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 1, Pages 195–224 (Mi izv631)  

This article is cited in 9 scientific papers (total in 9 papers)

The Cayley–Laplace differential operator on the space of rectangular matrices

S. P. Khekalo

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: This paper deals with the homogeneous Cayley–Laplace differential operator on the space of rectangular real matrices. Using Riesz potentials, we obtain fundamental solutions for this operator and some of its powers. We establish that the Cayley–Laplace operator satisfies the strong Huygens principle. Using intertwining operators with spectral parameters, we consider deformations of the Cayley–Laplace operator and find sufficient conditions under which these deformations satisfy the strong Huygens principle.

DOI: https://doi.org/10.4213/im631

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English version:
Izvestiya: Mathematics, 2005, 69:1, 191–219

Bibliographic databases:

MSC: 35A08, 35C05, 35Q53, 37K20, 14H70, 35L15
Received: 25.05.2004

Citation: S. P. Khekalo, “The Cayley–Laplace differential operator on the space of rectangular matrices”, Izv. RAN. Ser. Mat., 69:1 (2005), 195–224; Izv. Math., 69:1 (2005), 191–219

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. P. Khekalo, “Riesz potentials associated with the composite power function on the space of rectangular matrices”, J. Math. Sci. (N. Y.), 139:2 (2006), 6479–6490  mathnet  crossref  mathscinet  zmath  elib  elib
    2. Rubin B., “Riesz potentials and integral geometry in the space of rectangular matrices”, Adv. Math., 205:2 (2006), 549–598  crossref  mathscinet  zmath  isi  elib  scopus
    3. S. P. Khekalo, “Solution of the Hadamard problem in the class of stepwise gauge-equivalent deformations of homogeneous differential operators with constant coefficients”, St. Petersburg Math. J., 19:6 (2008), 1015–1028  mathnet  crossref  mathscinet  zmath  isi  elib
    4. Ournycheva E., Rubin B., “Semyanistyi's integrals and Radon transforms on matrix spaces”, J. Fourier Anal. Appl., 14:1 (2008), 60–88  crossref  mathscinet  zmath  isi  elib  scopus
    5. Ournycheva E., Rubin B., “Method of mean value operators for Radon transforms in the space of matrices”, Internat. J. Math., 19:3 (2008), 245–283  crossref  mathscinet  zmath  isi  elib  scopus
    6. Gonzalez F.B., “Invariant differential operators on matrix motion groups and applications to the matrix Radon transform”, Radon Transforms, Geometry, and Wavelets, Contemporary Mathematics Series, 464, 2008, 107–127  crossref  mathscinet  zmath  isi
    7. B. Rubin, “Funk, Cosine, and Sine Transforms on Stiefel and Grassmann Manifolds”, J Geom Anal, 2012  crossref  mathscinet  isi  scopus
    8. Caracciolo S., Sokal A.D., Sportiello A., “Algebraic/Combinatorial Proofs of Cayley-Type Identities for Derivatives of Determinants and Pfaffians”, Adv. Appl. Math., 50:4 (2013), 474–594  crossref  mathscinet  zmath  isi  scopus
    9. S. P. Khekalo, “Dunkl–Darboux differential-difference operators”, Izv. Math., 81:1 (2017), 156–178  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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