In this paper we consider the Heckman-Opdam-Jacobi operatorΔ_(H J)on R^(d+1).We define the Heckman-Opdam-Jacobi intertwining operator V_(H J),which turns out to be the transmutation operator betweenΔ_(H J)and the La...In this paper we consider the Heckman-Opdam-Jacobi operatorΔ_(H J)on R^(d+1).We define the Heckman-Opdam-Jacobi intertwining operator V_(H J),which turns out to be the transmutation operator betweenΔ_(H J)and the LaplacianΔ_(d+1).Next we construct^(t)V_(H J)the dual of this intertwining operator.We exploit these operators to develop a new harmonic analysis corresponding toΔ_(H J).展开更多
In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its...In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM^k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M^j(s), M^k(t)) for s, t ≤ n, M^j, M^k are g-twisted V modules, if V is g-rational.展开更多
We consider the harmonic analysis associated with the Dunkl operators on Rd. We study the Dunkl mean-periodic functions on the space ε(Rd) (the space of C∞-functions). We characterize also the continuous linear mapp...We consider the harmonic analysis associated with the Dunkl operators on Rd. We study the Dunkl mean-periodic functions on the space ε(Rd) (the space of C∞-functions). We characterize also the continuous linear mappings from ε(Rd) into itself which commute with the Dunkl operators.展开更多
文摘In this paper we consider the Heckman-Opdam-Jacobi operatorΔ_(H J)on R^(d+1).We define the Heckman-Opdam-Jacobi intertwining operator V_(H J),which turns out to be the transmutation operator betweenΔ_(H J)and the LaplacianΔ_(d+1).Next we construct^(t)V_(H J)the dual of this intertwining operator.We exploit these operators to develop a new harmonic analysis corresponding toΔ_(H J).
基金supported by National Natural Science Foundation of China(Grant Nos.11101269 and 11431010)
文摘In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM^k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M^j(s), M^k(t)) for s, t ≤ n, M^j, M^k are g-twisted V modules, if V is g-rational.
文摘We consider the harmonic analysis associated with the Dunkl operators on Rd. We study the Dunkl mean-periodic functions on the space ε(Rd) (the space of C∞-functions). We characterize also the continuous linear mappings from ε(Rd) into itself which commute with the Dunkl operators.
