Hadamards problem; generaliezd function; quantum groups; special functions.
Subject:
We apply the intertwining operators theory and the method of the Riesz kernels for the construction of the isohuygens deformations for the invariant differential operators. We established that strong Huygens principle holds for the Cayley–Laplaces differential operator on the space of the real rectangular matrixes. We constructed the fundamental solutions for this operator and its isohuygens deformations. The similar problem is solved for Gindikins differential operators associated with linear homogeneous cones.
Biography
Graduated from Faculty of Mathematics and Physics of Kolomna Teacher Training Institute in 1997. Ph.D. thesis was defended in 2001. The list of my works contains 8 titles.
Main publications:
Khekalo S. P., “Potentsialy Rissa v prostranstve pryamougolnykh matrits i izogyuigensova deformatsiya opertora Keli–Laplasa”, DAN, 376:2 (2001), 168–170
Khekalo S. P., “Fundamentalnoe reshenie iterirovannogo operatora tipa Keli–Gordinga”, UMN, 55:3 (2000), 191–192
Khekalo S. P., “Izogyuigensovy deformatsii odnorodnykh differentsialnykh operatorov, svyazannykh so spetsialnym konusom ranga tri”, Matematicheskie zametki, 70:6 (2001), 927–940
Khekalo S. P., “Funktsiya Besselya na konechnom pole”, Izvestiya vuzov, 2001, № 2(465), 79–82
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
S. P. Khekalo, “The heat equation on matrix space”, Zap. Nauchn. Sem. POMI, 332 (2006), 268–285; J. Math. Sci. (N. Y.), 142:6 (2007), 2671–2681
2005
4.
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
S. P. Khekalo, “The Igusa Zeta Function Associated with a Composite Power Function on the Space of Rectangular Matrices”, Mat. Zametki, 78:5 (2005), 773–791; Math. Notes, 78:5 (2005), 719–734
S. P. Khekalo, “Riesz potentials associated with the composite power function on the space of rectangular matrices”, Zap. Nauchn. Sem. POMI, 327 (2005), 207–225; J. Math. Sci. (N. Y.), 139:2 (2006), 6479–6490
8.
S. P. Khekalo, “Temporary deformations of degrees of the wave operator”, Zap. Nauchn. Sem. POMI, 324 (2005), 213–228; J. Math. Sci. (N. Y.), 138:2 (2006), 5603–5612
2004
9.
S. P. Khekalo, “The gauge related deformations of the ordinary linear differential operators with constant coefficients”, Zap. Nauchn. Sem. POMI, 308 (2004), 235–251; J. Math. Sci. (N. Y.), 132:1 (2006), 136–145
S. P. Khekalo, “Iso-Huygens deformations of the Cayley operator by the general Lagnese–Stellmacher potential”, Izv. RAN. Ser. Mat., 67:4 (2003), 189–212; Izv. Math., 67:4 (2003), 815–836
S. P. Khekalo, “Isohuygens deformation of the ultrahyperbolic operator”, Zap. Nauchn. Sem. POMI, 285 (2002), 207–223; J. Math. Sci. (N. Y.), 122:5 (2004), 3572–3581
S. P. Khekalo, “The Bessel function on a finite field”, Izv. Vyssh. Uchebn. Zaved. Mat., 2001, no. 2, 79–82; Russian Math. (Iz. VUZ), 45:2 (2001), 74–77
S. P. Khekalo, “Iso-Huygens Deformations of Homogeneous Differential Operators Related to a Special Cone of Rank 3”, Mat. Zametki, 70:6 (2001), 927–940; Math. Notes, 70:6 (2001), 847–859
S. P. Khekalo, “Fundamental solution for an iterated operator of Cayley–Garding type”, Uspekhi Mat. Nauk, 55:3(333) (2000), 191–192; Russian Math. Surveys, 55:3 (2000), 583–585
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