The linear symmetric systems associated with the modified Cherednik operators and applications

Hatem Mejjaoli[1]

  • [1] Department of Mathematics College of Sciences King Faisal University Ahsaa, Kingdom of Saudi Arabia

Annales mathématiques Blaise Pascal (2012)

  • Volume: 19, Issue: 1, page 213-245
  • ISSN: 1259-1734

Abstract

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We introduce and study the linear symmetric systems associated with the modified Cherednik operators. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite propagation speed property of it.

How to cite

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Mejjaoli, Hatem. "The linear symmetric systems associated with the modified Cherednik operators and applications." Annales mathématiques Blaise Pascal 19.1 (2012): 213-245. <http://eudml.org/doc/251046>.

@article{Mejjaoli2012,
abstract = {We introduce and study the linear symmetric systems associated with the modified Cherednik operators. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite propagation speed property of it.},
affiliation = {Department of Mathematics College of Sciences King Faisal University Ahsaa, Kingdom of Saudi Arabia},
author = {Mejjaoli, Hatem},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Modified Cherednik operators; modified Cherednik symmetric systems; energy estimates; finite speed of propagation; generalized wave equations with variable coefficients; modified Cherednik operators; well-posedness},
language = {eng},
month = {1},
number = {1},
pages = {213-245},
publisher = {Annales mathématiques Blaise Pascal},
title = {The linear symmetric systems associated with the modified Cherednik operators and applications},
url = {http://eudml.org/doc/251046},
volume = {19},
year = {2012},
}

TY - JOUR
AU - Mejjaoli, Hatem
TI - The linear symmetric systems associated with the modified Cherednik operators and applications
JO - Annales mathématiques Blaise Pascal
DA - 2012/1//
PB - Annales mathématiques Blaise Pascal
VL - 19
IS - 1
SP - 213
EP - 245
AB - We introduce and study the linear symmetric systems associated with the modified Cherednik operators. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite propagation speed property of it.
LA - eng
KW - Modified Cherednik operators; modified Cherednik symmetric systems; energy estimates; finite speed of propagation; generalized wave equations with variable coefficients; modified Cherednik operators; well-posedness
UR - http://eudml.org/doc/251046
ER -

References

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  1. N. Ben Salem, A. Ould Ahmed Salem, Convolution structure associated with the Jacobi-Dunkl operator on ℝ , Ramanujan J. 12 (2006), 359-378 Zbl1122.44002MR2293796
  2. J. Chazarain, A. Piriou, Introduction to the theory of linear partial differential equations, (1982), North-Holland Publishing Company Zbl0487.35002MR678605
  3. I. Cherednik, A unification of Knizhnik-Zamolodchnikove equations and Dunkl operators via affine Hecke algebras, Invent. Math. 106 (1991), 411-432 Zbl0725.20012MR1128220
  4. F. Chouchene, M. Mili, K. Trimèche, Positivity of the intertwining operator and harmonic analysis associated with the Jacobi-Dunkl operator on ℝ , Anal. and Appl. 1 (2003), 387-412 Zbl1056.43003MR2009310
  5. R. Courant, K. Friedrichs, H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik", Math. Ann. 100 (1928), 32-74 Zbl54.0486.01MR1512478
  6. K. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure and Appl. Math. 7 (1954), 345-392 Zbl0059.08902MR62932
  7. K. Friedrichs, Symmetric positive linear hyperbolic differential equations, Comm. Pure and Appl. Math. 11 (1958), 333-418 Zbl0083.31802MR100718
  8. K. Friedrichs, P. D. Lax, On symmetrizable differential operators, Proc. Symp. Pure Math. 9 (1967), 128-137 Zbl0184.36603MR239256
  9. P. D. Lax, On Cauchy’s problem for hyperbolic equations and the differentiability of solutions of elliptic equations, Comm. Pure and Appl. Math. 8 (1955), 615-633 Zbl0067.07502MR78558
  10. P. D. Lax, R. S. Phillips, Local boundary conditions for dissipative symmetric linear differential operators, Comm. Pure and Appl. Math. 13 (1960), 427-455 Zbl0094.07502MR118949
  11. G. Lebeau, Majeure d’équations aux dérivées partielles, Prépublication de l’école polytechniques 28 (1990), 43-62 
  12. Eric M. Opdam, Harmonic analysis for certain representations of graded Hecke algebras, Acta Math. 175 (1995), 75-121 Zbl0836.43017MR1353018
  13. Eric M. Opdam, Lecture notes on Dunkl operators for real and complex reflection groups, 8 (2000), Mathematical Society of Japan, Tokyo Zbl0984.33001MR1805058
  14. J. Rauch, L 2 is a continuable initial condition for Kreiss’ mixed problems, Comm. Pure. and Appl. Math. 15 (1972), 265-285 Zbl0226.35056MR298232
  15. B. Schapira, Contributions to the hypergeometric function theory of Heckman and Opdam: sharpe stimates, Schwartz spaces, heat kernel, Geom. Funct. Anal. 18 (2008), 222-250 Zbl1147.33004MR2399102
  16. T. Shirota, On the propagation speed of a hyperbolic operator with mixed boundary conditions, J. Fac. Sci. Hokkaido Univ. 22 (1972), 25-31 Zbl0234.35060MR304871
  17. H. Triebel, Interpolation theory, functions spaces differential operators, (1978), North Holland, Amesterdam Zbl0387.46032
  18. H. Weber, Die partiellen Differentialgleichungen der mathematischen Physik nach Riemann’s Vorlesungen in 4-ter Auflage neu bearbeitet, Braunschweig, Friederich Vieweg 1 (1900), 1-390 Zbl31.0745.01
  19. S. Zaremba, Sopra un theorema d’unicità relativo alla equazione delle onde sferiche, Rend. Accad. Naz. Lincei 24 (1915), 904-908 Zbl45.0566.01

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