论文标题
Octonionic Bergman和SzegöKernels的最新和新结果
Recent and new results on octonionic Bergman and Szegö kernels
论文作者
论文摘要
最近，人们已经开始在八世代单基因函数的情况下研究Bergman和SzegöKernels。特别是，已经建立了八元离子单位球的伯格曼内核的明确配方，以及八元离子右半空间的明确公式以及八元离子单位球的SzegöKernel的公式。在本文中，我们通过为$ {\ cal {s}}形式的szegöKernel开发明确的公式来扩展这一调查，：= \ {z \ in \ mathbb {o} \ mathbb {o} \ mid 0 <\ re（z）<d \ i（z）<d \} $，我们通过限制$ d \ d \ d off ty $ d.八元离子右半空间。此外，我们为此类带状域的Bergman内核设置了公式，并将两个核相互关联。实际上，这些内核函数可以分别以固定函数和cotangent函数分别以周期性的八元离子单基因概括来表示。
Very recently one has started to study Bergman and Szegö kernels in the setting of octonionic monogenic functions. In particular, explicit formulas for the Bergman kernel for the octonionic unit ball and for the octonionic right half-space as well as a formula for the Szegö kernel for the octonionic unit ball have been established. In this paper we extend this line of investigation by developing explicit formulas for the Szegö kernel of strip domains of the form ${\cal{S}} := \{z \in \mathbb{O} \mid 0 < \Re(z) < d\}$ from which we derive by a limit argument considering $d \to \infty$ the Szegö kernel of the octonionic right half-space. Additionally, we set up formulas for the Bergman kernel of such strip domains and relate both kernels with each other. In fact, these kernel functions can be expressed in terms of one-fold periodic octonionic monogenic generalizations of the cosecant function and the cotangent function, respectively.
