Hilbert Transforms Associated with Dunkl-Hermite Polynomials

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2009
• Hauptverfasser: Ben Salem, Nejib, Samaali, Taha
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2009
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/149169
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Hilbert Transforms Associated with Dunkl-Hermite Polynomials / N.B. Salem, T. Samaali // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 12 назв. — англ.

We consider expansions of functions in Lp(R,|x|2kdx), 1 ≤ p < +∞ with respect to Dunkl-Hermite functions in the rank-one setting. We actually define the heat-diffusion and Poisson integrals in the one-dimensional Dunkl setting and study their properties. Next, we define and deal with Hilbert...