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Warianty tytułu
Języki publikacji
Abstrakty
We derive differential relations between the Dunkl spherical and solid means of continuous functions. Next we use the relations to give inductive proofs of mean-value properties for the Dunkl polyharmonic functions and their converses.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
655--664
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
- Polish Academy of Sciences Institute of Mathematics Śniadeckich 8, 00-656 Warsaw, Poland
- Jan Kochanowski University Faculty of Mathematics and Natural Sciences ul. Świętokrzyska 15, 25-406 Kielce, Poland
Bibliografia
- [1] E.F. Beckenbach, M. Reade, Mean values and harmonic polynomials, Trans. Amer. Math. Soc. 51 (1945), 240-245.
- [2] C.F. Dunkl, Reflection groups and orthogonal polynomials on the sphere, Math. Z. 197 (1988), 33-60.
- [3] C.F. Dunkl, Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc. 311 (1989), 167-183.
- [4] C.F. Dunkl, Operators commuting with Goxeter group action on polynomials, [in:] Invariant Theory and Tableaux, IMA Vol. Math. Appl. 19, Springer-Verlag, 1990, 107-117.
- [5] C.F. Dunki, Reflection groups in analysis and applications, Japan J. Math. 3 (2008), 215-246.
- [6] C.F. Dunkl, Y. Xu, Ortogonal Polynomials of Several Variables, Cambridge Univ. Press, 2001.
- [7] K. Hassine, Mean value property associated with the Dunkl Laplacian, http://arxiv.org/pdf/1401.1949.pdf
- [8] G. Łysik, On the mean-value property for polyharmonic functions, Acta Math. Hungar. 133 (2011), 133-139.
- [9] M. Maslouhi, On the generalized Poisson transform, Integral Transforms Spec. Func. 20 (2009), 775-784.
- [10] M. Maslouhi, E.H. Youssfi, Harmonic functions associated to Dunkl operators, Monatsh. Math. 152 (2007), 337-345.
- [11] M. Maslouhi, R. Daher, Weil's lemma and converse mean value for Dunkl operators, [in:] Operator Theory Adv. Math. 205, Birkhauser, 2009, 91-100.
- [12] H. Mejjaoli, K. Trimeche, On a mean value property associated with the Dunkl Laplacian operator and applications, Integral Transforms Spec. Func. 12 (2001), 279-302.
- [13] M. Rosier, Positivity of Dunkl's intertwining operator, Duke Math. J. 98 (1999), 445-463.
- [14] M. Rosier, A positivity radial product formula for the Dunkl kernel, Trans. Amer. Math. Soc. 355 (2003), 2413-2438.
- [15] N.B. Salem, K. Touahri, Pizzetti series and polyharmonicity associated with the Dunkl Laplacian, Mediterr. J. Math. 7 (2010), 455-470.
- [16] N.B. Salem, K. Touahri, Cubature formulae associated with the Dunkl Laplacian, Results Math. 58 (2010), 119-144.
- [17] K. Trimeche, The Dunkl intertwining operator on spaces of functions and distributions and integral representation of its dual, Integral Transform Spec. Func. 12 (2001), 349-374.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-aba14ee0-0d9b-461f-b208-5ecd9f42f632