Essential spectra of tensor product Hilbert complexes, and the $\overline\partial$-Neumann problem on product manifolds

Autor:	Berger, Franz
Rok vydání:	2015
Předmět:	Mathematics - Spectral Theory Mathematics - Analysis of PDEs Mathematics - Complex Variables Mathematics - Functional Analysis Primary 58J50 Secondary 35N15 58J10 47A13
Druh dokumentu:	Working Paper
DOI:	10.1016/j.jfa.2016.06.004
Popis:	We investigate tensor products of Hilbert complexes, in particular the (essential) spectrum of their Laplacians. It is shown that the essential spectrum of the Laplacian associated to the tensor product complex is computable in terms of the spectra of the factors. Applications are given for the $\overline\partial$-Neumann problem on the product of two or more Hermitian manifolds, especially regarding (non-) compactness of the associated $\overline\partial$-Neumann operator. Comment: 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1508.01749 Zobrazit plný text záznamu View this record from Arxiv