论文标题
加权的Quaternionic Cauchy奇异积分
Weighted quaternionic Cauchy singular integral
论文作者
论文摘要
我们研究了加权Quaternionic Cauchy转换的某些光谱特性，当作用于高斯集成函数的右Quaternionic Hilbert空间。我们研究了其限制性，紧凑性和成员资格，并向$ k $ schatten班级学习，并确定了它的范围。这是通过限制第二种n-s-polyregular bargmann空间来完成的，为此，我们为其在quaternionicitô---荷铁矿多项式中为其作用提供明确的闭合表达，以构成正交基础。我们还表现出其n-bergman投影的本征函数的正交基础，从而明确确定其奇异值。所获得的结果将加权的cauchy在复杂平面上转变为Quaternionic设置的结果概括。
We investigate some spectral properties of the weighted quaternionic Cauchy transform when acting on the right quaternionic Hilbert space of Gaussian integrable functions. We study its boundedness, compactness, and memberships to the $k$-Schatten class, and we identify its range. This is done by means of its restriction to the n-th S-polyregular Bargmann space of the second kind, for which we provide an explicit closed expression for its action on the quaternionic Itô--Hermite polynomials constituting an orthogonal basis. We also exhibit an orthogonal basis of eigenfunctions of its n-Bergman projection leading to the explicit determination of its singular values. The obtained results generalize those given for weighted Cauchy transform on the complex plane to the quaternionic setting.
