Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on ℂ n

Given a principal value convolution on the Heisenberg group H _n = ? ⁿ × ?, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on ? ⁿ . We also calculate the Dirichlet kernel for the Laguerre expansion on the group H _n .     

Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on ?n

Given a principal value convolution on the Heisenberg group H _n = ℂ ⁿ × ℝ, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on ℂ ⁿ . We also calculate the Dirichlet kernel for the Laguerre expansion on the group H _n . Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

Multiplier theorems for special Hermite expansions on Cn

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Laguerre matrix polynomial series expansion: Theory and computer applications

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In this paper, a class of biholomorphic mappings named quasi-convex mapping of order a in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order a defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.     

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