Second-Order-Optimal Minimum-Energy Filters on Lie Groups

Some Second-order Partial Differential Equations Associated with Lie Groups

In this note we survey results in recent research papers on the use of Lie groups in the study of partial differential equations. The focus will be on parabolic equations, and we will show how the problems at hand have solutions that seem natural in the context of Lie groups. The research is joint with D.W. Robinson, as well as other researchers who are listed in the references.

Optimal Design of Second-Order Linear Filters for Control Charting

In many common control charting situations, the statistic to be charted can be viewed as the output of a linear filter applied to the sequence of process measurement data. In recent work that has generalized this concept, the charted statistic is the output of a general linear filter in impulse response form, and the filter is designed by selecting its impulse response coefficients to optimize ...

Second-order Subelliptic Operators on Lie Groups Ii: Real Measurable Principal Coeecients

Let G be a connected Lie group with Lie algebra g and a 1 ; : : : ; a d 0 an algebraic basis of g. Further let A i denote the generators of left translations, acting on the L p-spaces L p (G ; dg) formed with left Haar measure dg, in the directions a i. We consider second-order operators

SEMINAR ON LIE GROUPS 1. Lie Groups

Example 1.3. (R,+) Example 1.4. S or T n = S × ...× S Example 1.5. Gl (n,F) ⊆ F, where F = R or C Example 1.6. E3 = isometries of R (2 connected components) Let the orthogonal group O3 < E3 be the subgroup that fixes the origin, and let the special orthogonal group SO (3) = SO3 < O3 be the orientation-preserving elements of O3. Visualizing SO (3): Let u be a vector of length l in R, correspondi...

On Lie Group Classification of Second{order Ordinary Difference Equations