TY - JOUR
T1 - Intertwining Operators Associated to a Family of Differential-Reflection Operators
AU - Ben Said, Salem
AU - Boussen, Asma
AU - Sifi, Mohamed
N1 - Publisher Copyright:
© 2016, Springer International Publishing.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - We introduce a family of differential-reflection operators Λ A , ε acting on smooth functions defined on R. Here, A is a Sturm–Liouville function with additional hypotheses and - 1 ≤ ε≤ 1. For special pairs (A, ε) , we recover Dunkl’s, Heckman’s and Cherednik’s operators (in one dimension). The spectral problem for the operators Λ A , ε is studied. In particular, we obtain suitable growth estimates for the eigenfunctions of Λ A , ε. As the operators Λ A , ε, are a mixture of d / d x and reflection operators, we prove the existence of an intertwining operator VA , ε between Λ A , ε and the usual derivative. The positivity of VA , ε is also established.
AB - We introduce a family of differential-reflection operators Λ A , ε acting on smooth functions defined on R. Here, A is a Sturm–Liouville function with additional hypotheses and - 1 ≤ ε≤ 1. For special pairs (A, ε) , we recover Dunkl’s, Heckman’s and Cherednik’s operators (in one dimension). The spectral problem for the operators Λ A , ε is studied. In particular, we obtain suitable growth estimates for the eigenfunctions of Λ A , ε. As the operators Λ A , ε, are a mixture of d / d x and reflection operators, we prove the existence of an intertwining operator VA , ε between Λ A , ε and the usual derivative. The positivity of VA , ε is also established.
KW - Differential-reflection operators
KW - intertwining operators
KW - spectral problem
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U2 - 10.1007/s00009-016-0736-2
DO - 10.1007/s00009-016-0736-2
M3 - Article
AN - SCOPUS:84969872780
SN - 1660-5446
VL - 13
SP - 4129
EP - 4151
JO - Mediterranean Journal of Mathematics
JF - Mediterranean Journal of Mathematics
IS - 6
ER -