5 papers
Elliptic operators on infinite graphs
J. Dodziuk
We present some applications of ideas from partial differential equations and differential geometry to the study of difference equations on infinite graphs. All operators that we c…
Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians
Jozef Dodziuk, Varghese Mathai
In this paper, a discrete form of the Kato inequality for discrete magnetic Laplacians on graphs is used to study asymptotic properties of the spectrum of discrete magnetic Schrodi…
Arithmetic properties of eigenvalues of generalized Harper operators on graphs
J. Dodziuk, V. Mathai, S. Yates
Let $\Qbar$ denote the field of complex algebraic numbers. A discrete group is said to have the -multiplier algebraic eigenvalue property, if for every matrix with entri…
Integral Structures on H-type Lie Algebras
G. Crandall, J. Dodziuk
In this paper we prove that every H-type Lie algebra possesses a basis with respect to which the structure constants are integers. Existence of such an integral basis implies via t…
Approximating torsion on amenable covering spaces
Jozef Dodziuk, Varghese Mathai, Stuart Yates
It was pointed out to us that the proof of a crucial lemma (Lemma 5.3) in the paper is incorrect. Thus the approximation theorem (Theorem 0.1) for L^2 torsion of an amenable coveri…