Back to Search
Start Over
A Criterion for Essential Self-Adjointness of a Symmetric Operator Defined by Some Infinite Hermitian Matrix with Unbounded Entries.
- Source :
- Integral Equations & Operator Theory; Oct2015, Vol. 83 Issue 2, p231-242, 12p
- Publication Year :
- 2015
-
Abstract
- We shall consider a double infinite, Hermitian, complex entry matrix $${A=[a_{x,y}]_{x,y\in\mathbb{Z}}}$$ . In the present note we give a criterion, expressed in terms of the entries of the matrix, for the corresponding symmetric operator defined on compactly supported sequences, to be essentially self-adjoint in the space $${\ell_2(\mathbb{Z})}$$ . Roughly speaking, assuming that x denotes the row number, we require that: (1) there exist $${\gamma\in[0,1)}$$ and n > 0 for which the entries that are at distance larger than $${n(|x|^2+1)^{\gamma/2}}$$ from the diagonal vanish and (2) the $${\ell^1}$$ norm of the xth row grows slower that $${|x|^{\gamma-1}}$$ , as $${|x|\to+\infty}$$ . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0378620X
- Volume :
- 83
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Integral Equations & Operator Theory
- Publication Type :
- Academic Journal
- Accession number :
- 110138805
- Full Text :
- https://doi.org/10.1007/s00020-015-2237-2