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Volumn 97, Issue , 2005, Pages 25-55

Convolution operator and maximal function for the Dunkl transform

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EID: 33644958362     PISSN: 00217670     EISSN: 15658538     Source Type: Journal    
DOI: 10.1007/BF02807401     Document Type: Article
Times cited : (210)

References (23)
  • 1
    • 84963950040 scopus 로고
    • Differential-difference operators associated to reflection groups
    • C. F. Dunkl, Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc. 311 (1989), 167-183.
    • (1989) Trans. Amer. Math. Soc. , vol.311 , pp. 167-183
    • Dunkl, C.F.1
  • 2
    • 0001195479 scopus 로고
    • Integral kernels with reflection group invariance
    • C. F. Dunkl, Integral kernels with reflection group invariance, Canad. J. Math. 43 (1991), 1213-1227.
    • (1991) Canad. J. Math. , vol.43 , pp. 1213-1227
    • Dunkl, C.F.1
  • 3
    • 0001174037 scopus 로고
    • Hankel transforms associated to finite reflection groups
    • Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications (Tampa, FL, 1991), Amer. Math. Soc., Providence, RI
    • C. F. Dunkl, Hankel transforms associated to finite reflection groups, in Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications (Tampa, FL, 1991), Contemporary Mathematics 138, Amer. Math. Soc., Providence, RI, 1992, pp. 123-138.
    • (1992) Contemporary Mathematics , vol.138 , pp. 123-138
    • Dunkl, C.F.1
  • 4
    • 0000271828 scopus 로고    scopus 로고
    • Intertwining operators and polynomials associated with the symmetric group
    • C. F. Dunkl, Intertwining operators and polynomials associated with the symmetric group, Monatsh. Math. 126 (1998), 181-209.
    • (1998) Monatsh. Math. , vol.126 , pp. 181-209
    • Dunkl, C.F.1
  • 7
    • 0000945341 scopus 로고
    • The Dunkl transform
    • M. F. E. de Jeu, The Dunkl transform, Invent. Math. 113 (1993), 147-162.
    • (1993) Invent. Math. , vol.113 , pp. 147-162
    • De Jeu, M.F.E.1
  • 8
    • 84871112635 scopus 로고    scopus 로고
    • Paley-Wiener theorems for the Dunkl transform
    • to appear. ArXiv:math.CA/0404439
    • M. F. E. de Jeu, Paley-Wiener theorems for the Dunkl transform, Trans. Amer. Math. Soc., to appear. ArXiv:math.CA/0404439.
    • Trans. Amer. Math. Soc.
    • De Jeu, M.F.E.1
  • 9
    • 0000064759 scopus 로고
    • A new proof of a paley-wiener theorem for the Jacobi transform
    • T. H. Koornwinder, A new proof of a Paley-Wiener theorem for the Jacobi transform, Ark. Mat. 13 (1975), 145-159.
    • (1975) Ark. Mat. , vol.13 , pp. 145-159
    • Koornwinder, T.H.1
  • 10
    • 0010750097 scopus 로고    scopus 로고
    • On a mean value property associated with the Dunkl Laplacian operator and applications
    • H. Mejjaoli and K. Trimèche, On a mean value property associated with the Dunkl Laplacian operator and applications, Integral Transform. Spec. Funct. 12 (2001), 279-302.
    • (2001) Integral Transform. Spec. Funct. , vol.12 , pp. 279-302
    • Mejjaoli, H.1    Trimèche, K.2
  • 11
    • 0002552020 scopus 로고
    • Bessel-type signed hypergroups on R
    • (Oberwolfach 1994) (H. Heyer and A. Mukherjea, eds.), World Scientific, Singapore
    • M. Rösler, Bessel-type signed hypergroups on R, in Probability Measures on Groups and Related Structures, XI (Oberwolfach 1994) (H. Heyer and A. Mukherjea, eds.), World Scientific, Singapore, 1995, pp. 292-304.
    • (1995) Probability Measures on Groups and Related Structures, XI , pp. 292-304
    • Rösler, M.1
  • 12
    • 0038707723 scopus 로고    scopus 로고
    • Generalized Hermite polynomials and the heat equation for Dunkl operators
    • M. Rösler, Generalized Hermite polynomials and the heat equation for Dunkl operators, Comm. Math. Phys. 192 (1998), 519-542.
    • (1998) Comm. Math. Phys. , vol.192 , pp. 519-542
    • Rösler, M.1
  • 13
    • 0001701379 scopus 로고    scopus 로고
    • Positivity of Dunkl's intertwining operator
    • M. Rösler, Positivity of Dunkl's intertwining operator, Duke Math. J. 98 (1999), 445-463.
    • (1999) Duke Math. J. , vol.98 , pp. 445-463
    • Rösler, M.1
  • 14
    • 33644953643 scopus 로고    scopus 로고
    • One-parameter semigroups related to abstract quantum models of Calogero type
    • (H. Heyer, T. Hirai and N. Obata, eds.), Gräbner, Altendorf
    • M. Rösler, One-parameter semigroups related to abstract quantum models of Calogero type, in Infinite Dimensional Harmonic Analysis (Kyoto, 1999) (H. Heyer, T. Hirai and N. Obata, eds.), Gräbner, Altendorf, 2000, pp. 290-305.
    • (2000) Infinite Dimensional Harmonic Analysis (Kyoto, 1999) , pp. 290-305
    • Rösler, M.1
  • 15
    • 0038030889 scopus 로고    scopus 로고
    • A positive radial product formula for the Dunkl kernel
    • M. Rösler, A positive radial product formula for the Dunkl kernel, Trans. Amer. Math. Soc. 355 (2003), 2413-2438.
    • (2003) Trans. Amer. Math. Soc. , vol.355 , pp. 2413-2438
    • Rösler, M.1
  • 16
    • 0002327987 scopus 로고    scopus 로고
    • Markov processes associated with Dunkl operators
    • M. Rösler and M. Voit, Markov processes associated with Dunkl operators, Adv. in Appl. Math. 21 (1998), 575-643.
    • (1998) Adv. in Appl. Math. , vol.21 , pp. 575-643
    • Rösler, M.1    Voit, M.2
  • 19
    • 0036486867 scopus 로고    scopus 로고
    • Paley-wiener theorems for the Dunkl transform and Dunkl translation operators
    • K. Trimèche, Paley-Wiener theorems for the Dunkl transform and Dunkl translation operators, Integral Transform. Spec. Funct. 13 (2002), 17-38.
    • (2002) Integral Transform. Spec. Funct. , vol.13 , pp. 17-38
    • Trimèche, K.1
  • 21
    • 0040361697 scopus 로고    scopus 로고
    • Integration of the intertwining operator for h-harmonic polynomials associated to reflection groups
    • Yuan Xu, Integration of the intertwining operator for h-harmonic polynomials associated to reflection groups, Proc. Amer. Math. Soc. 125 (1997), 2963-2973.
    • (1997) Proc. Amer. Math. Soc. , vol.125 , pp. 2963-2973
    • Xu, Y.1
  • 22
    • 0036699936 scopus 로고    scopus 로고
    • An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials
    • Yuan Xu, An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials, Adv. in Appl. Math. 29 (2002), 328-343.
    • (2002) Adv. in Appl. Math. , vol.29 , pp. 328-343
    • Xu, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.