Grounding in communication

Grounding in communication (1991)

by G. A. Hunt

Venue:	In
Citations:	538 - 10 self

Datum	Value	Source
TITLE	Grounding in communication	INFERENCE
AUTHOR NAME	G. A. Hunt	SVM HeaderParse 0.2
AUTHOR ADDR	Princeton, New Jersey 08540.	SVM HeaderParse 0.2
ABSTRACT	We give a general analysis of a class of pairs of positive self-adjoint operators A and B for which A + XB has a limit (in strong resolvent sense) as h-10 which is an operator A, # A! Recently, Klauder [4] has discussed the following example: Let A be the operator-(d2/A2) + x2 on L2(R, dx) and let B = 1 x 1-s. The eigenvectors and eigenvalues of A are, of course, well known to be the Hermite functions, H,(x), n = 0, l,... and E, = 2n + 1. Klauder then considers the eigenvectors of A + XB (A> 0) by manipulations with the ordinary differential equation (we consider the domain questions, which Klauder ignores, below). He finds that the eigenvalues E,(X) and eigenvectors &(A) do not converge to 8, and H, but rather AO) + (en 4 Ho+, J%(X)-+ gn+1 I n = 0, 2,..., We wish to discuss in detail the general phenomena which Klauder has uncovered. We freely use the techniques of quadratic forms and strong resolvent convergence; see e.g. [3], [5]. Once one decides to analyze Klauder’s phenomenon in the language of quadratic forms, the phenomenon is quite easy to understand and control. In fact, the theory is implicit in Kato’s book [3, VIII.31.	SVM HeaderParse 0.2
YEAR	1991	INFERENCE
VENUE	In	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
CITATIONS	7 found	ParsCit 1.0