论文标题
Q划分的Askey-Wilson积分和相关的操作员
q-Fractional Askey-Wilson Integrals and Related Semigroups of Operators
论文作者
论文摘要
我们介绍了三个单参数的操作员，并确定其光谱。其中两个是与Askey-Wilson操作员相关的分数积分。我们还将这些家庭研究为正线性近似算子的家庭。应用包括Askey-Wilson多项式的连接关系和双线性公式。我们还引入了Q-Gauss-WeierStrass变换，并证明了它的表示和反转定理。
We introduce three one-parameter semigroups of operators and determine their spectra. Two of them are fractional integrals associated with the Askey-Wilson operator. We also study these families as families of positive linear approximation operators. Applications include connection relations and bilinear formulas for the Askey-Wilson polynomials. We also introduce a q-Gauss-Weierstrass transform and prove a representation and inversion theorem for it.
