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

Disenfranchisement of the College Student Vote: When a Resident is not a Resident

The standards used by state and local election officials to determine whether students may vote as residents of the communities in which they attend college vary significantly among the fifty states. Two fundamental rights conflict in determining whether college students should be entitled to vote as residents of their college communities: the right of students to equal protection of the laws and eh right of states to limit the right to vote to bona fide residents. This Comment demonstrates the need for the education of election officials and college students in the common law principles of domicile. Moreover, it will conclude that uniform voting residency standards and more efficient and comprehensive absentee-ballot voting systems are essential to the effective enfranchisement of students, a major congressional consideration in the passage of the twenty-sixth amendment

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