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1.
《Integral Transforms and Special Functions》2012,23(2):105-123
We work out the expression of the generalized Bessel function of B 2-type derived in [N. Demni, Radial Dunkl processes associated with Dihedral systems. Séminaire de Probabilités XLII]. This is done using Dijksma and Koornwinder's product formula for Jacobi polynomials [A. Dijksma and T.H. Koornwinder, Spherical Harmonics and the product of two Jacobi polynomials, Indag. Math. 33 (1971), pp. 191–196], and the obtained expression is given by multiple integrals involving only a normalized modified Bessel function and two symmetric Beta distributions. We think of that expression as the major step towards the explicit expression of the Dunkl's intertwining operator V k in the B 2-invariant setting. Finally, we give in the same setting an explicit formula for the action of V k on a product of |y|2κ, κ≥0, and the ordinary spherical harmonic Y 4m (y):=|y|4m cos(4mθ), y=|y|e iθ. The obtained formula extends to all dihedral systems and it improves the one derived in [Y. Xu, Intertwining operator and h-harmonics associated with reflection group, Can. J. Math. 50 (1998), pp. 193–209]. 相似文献
2.
The purpose of this paper is to derive quadrature estimates on compact, homogeneous manifolds embedded in Euclidean spaces, via energy functionals associated with a class of group-invariant kernels which are generalizations of zonal kernels on the spheres or radial kernels in euclidean spaces. Our results apply, in particular, to weighted Riesz kernels defined on spheres and certain projective spaces. Our energy functionals describe both uniform and perturbed uniform distribution of quadrature point sets. 相似文献
3.
We extend the uncertainty principle, the Cowling-Price theorem, on noncompact Riemannian symmetric spacesX. We establish a characterization of the heat kernel of the Laplace-Beltrami operator onX from integral estimates of the Cowling-Price type. 相似文献
4.
A celebrated theorem of Coburn asserts that, on the setting of the Hardy space, if a Toeplitz operator is nonzero, then either it is one-to-one or its adjoint operator is one-to-one. In this paper, we show that an analogous result holds for Toeplitz operators acting on the Dirichlet space. 相似文献