Spherical Functions on Euclidean Space

We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space $E^n = G/K$ where $G$ is the semidirect product $R^n \cdot K$ of the translation group with a closed subgroup $K$ of the orthogonal group O(n). We give exact parameterizations of the space of $(G,K)$--spherical functions by a certain affine algebraic variety, and of the positive definite ones by a real form of that variety. We give exact formulae for the spherical functions in the case where $K$ is transitive on the unit sphere in $E^n$.Comment: 10 page

Fair or Foul?: SEC Administrative Proceedings and Prospects for Reform Through Removal Legislation

This Article catalogues the long list of criticisms of the Commission’s administrative proceedings. It also evaluates data describing the outcome of litigated matters and finds that, with the exception of insider trading cases, the Commission has an exceptionally high and statistically indistinguishable record of success in administrative and federal court proceedings alike. The data thus seem not to support the view that the Commission has a generalized home-court advantage in administrative proceedings. Nonetheless, the Commission’s virtually unfettered discretion in forum selection decisions, when it can assign cases to a forum that it controls, raises a plethora of institutional design concerns

Convention on International Liability for Damage Caused by Space Objects: Definition and Determination of Damages After the Cosmos 954 Incident

This Note examines the conflicting provisions of the Liability Convention in the context of the Cosmos 954 incident to determine whether the damages that Canada claimed would be recoverable under the Convention. The analysis will illustrate the need for change in the Liability Convention\u27s definition of the measure of damages. Finally, this Note presents a proposal that would render the provisions more consistent with the spirit and the purpose of the Liability Convention

Stepwise Square Integrability for Nilradicals of Parabolic Subgroups and Maximal Amenable Subgroups

In a series of recent papers we extended the notion of square integrability, for representations of nilpotent Lie groups, to that of stepwise square integrability. There we discussed a number of applications based on the fact that nilradicals of minimal parabolic subgroups of real reductive Lie groups are stepwise square integrable. Here, in Part I, we prove stepwise square integrability for nilradicals of arbitrary parabolic subgroups of real reductive Lie groups. This is technically more delicate than the case of minimal parabolics. We further discuss applications to Plancherel formulae and Fourier inversion formulae for maximal exponential solvable subgroups of parabolics and maximal amenable subgroups of real reductive Lie groups. Finally, in Part II, we extend a number of those results to (infinite dimensional) direct limit parabolics. These extensions involve an infinite dimensional version of the Peter-Weyl Theorem, construction of a direct limit Schwartz space, and realization of that Schwartz space as a dense subspace of the corresponding $L^2$ space.Comment: The proof of Theorem 5.9 is improved, several statements are clarified, and a certain number of typographical errors are correcte

Book Review: Deforming Tort Reform

The storms buffeting the tort system over the past two decades have come in three distinct waves. In the late 1960s, steep increases in the insurance costs incurred by health care providers protecting against negligence claims by patients triggered what came to be known as the medical malpractice crisis. In the mid-1970s, manufacturers whose liability insurance premiums suddenly soared raised obstreperous complaints that called public attention to the existence of a product liability crisis. Finally, other groups whose activities created risks exposing them to lawsuits found that their liability insurance rates had also risen precipitously. A full-blown torts crisis was at hand. The common law of torts attracted a major share of the blame for each of the three crises. Observers blamed the medical malpractice crisis on judicial decisions that expanded the doctrine of res ipsa loquitur by permitting juries to infer negligence from the mere occurrence of an untoward result following medical treatment, and that recognized a duty of due care by physicians to disclose the risk of treatment to patients. Members of Congress, among others, blamed the product liability crisis on state-by-state variations in rules governing the obligations of manufacturers and sellers. Working groups formed to study the issue found the across-the-board torts crisis attributable to the erosion of fault as the basis for liability and the adoption of rules and practices that were allegedly responsible for undue increases in compensatory as well as punitive damage awards. As a consequence, those adversely affected by rising insurance costs demanded, and often achieved, what they called tort reform. Responding to pressure, states enacted pro-defendant legislative adjustments to common law rules of medical malpractice, products liability, and general tort law. By equating tort reform with unidirectional statutory modification of the common law, its advocates succeeded in investing the term with a politically useful, if skewed, meaning. Until the dawn of the present age of tort-related crises, the notion of tort reform was likely to evoke images of a movement to change pro-defendant common law rules so that injured plaintiffs could more easily win judgments or recover full damages. Indeed, through the first half of the twentieth century, the tort system tended to protect the interests of defendants in general as well as particular categories of defendants. What might be called the old tort reform was partly an effort to rectify these imbalances