欧几里得空间中Hodge-de Rham系统的Fischer分解

欧几里得空间中Hodge-de Rham系统的正交Appell基

Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces

最近，在欧几里得空间R^m中，对于Hodge-de Rham系统的k-齐次多项式解的空间，给出了正交基的Gelfand-Tsetlin构造.在本文中，我们给出了这些基的另一种结构，主要是，我们证明了基甚至形成完全正交Appell系统。此外，我们还研究了相应的泰勒级数展开式。作为应用，我们构造了任意广义Moisil-Theodoresco系统齐次解的显式正交基.

欧几里得空间中Hodge-de Rham系统的Gelfand-Tsetlin基

The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces

本文的主要目的是为欧几里得空间R^m中Hodge-de Rham系统的k-齐次多项式解空间构造取s-向量空间值的显式正交基。实际上，我们甚至用盖根堡多项式来描述这种空间的所谓的Gelfand-Tsetlin基。作为应用，我们得到了R^m中广义Moisil-Theodoresco方程组齐次解空间的正交基的计算方法.

广义Moisil-Theodoresco系统和Hodge-de Rham系统的多项式解

On polynomial solutions of generalized Moisil-Theodoresco systems and Hodge-de Rham systems

研究广义Moisil-Theodoresco（GMT）系统的多项式解与Hodge-de Rham系统的多项式解之间的关系，并利用这些关系描述GMT系统的多项式解.我们将GMT系统的齐次解空间在群O（m）的作用下分解成不可约的块，并用它们的最高权来刻画各个块，计算它们的维数.

Towards a L 2 cohomology theory for Hodge modules on infinite covering spaces: L 2 constructible cohomology and L 2 de Rham cohomology for coherent D-modules

This article constructs Von Neumann invariants for constructible complexes and coherent D-modules on compact complex manifolds, generalizing the work of the author on coherent L 2-cohomology. We formulate a conjectural generalization of Dingoyan's L 2-Mixed Hodge structures in terms of Saito's Mixed Hodge Modules and give partial results in this direction. 2020 AMS Classification: 32J27.

Frölicher spectral sequence and Hodge structures on the cohomology of complex parallelisable manifolds

For complex parallelisable manifolds $Γ\backslash G$, with $G$ a solvable or semisimple complex Lie group, the Frölicher spectral sequence degenerates at the second page. In the solvable case, the de-Rham cohomology carries a pure Hodge structure. In contrast, in the semisimple case, purity depends on the lattice, but there is always a direct summand of the de Rham cohomology which does carry a pure Hodge structure and is independent of the lattice.

Harmonic forms and the Rumin complex on Sasakian manifolds

We show that the kernel of the Rumin Laplacian agrees with that of the Hodge-de Rham Laplacian on compact Sasakian manifolds. As a corollary, we obtain another proof of primitiveness of harmonic forms. Moreover, the space of harmonic forms coincides with the sub-Riemann limit of Hodge-de Rham Laplacian when its limit converges. Finally, we express the analytic torsion function associated with the Rumin complex in terms of the Reeb vector field.