On Casimir's theorem of semi-simple continuous groups

A Theorem on Semi-Continuous Functions

A Theorem on Semi - Continuous Functions

RECENTLY G. C. Young* and A. Denjoyf have communicated theorems—those in Denjoy's memoir are of an especially comprehensive character—dealing, in particular, with point sets where the four derivatives of a given continuous function are identical. It is the purpose of this note to treat an analogous problem that arises when "derivative" is replaced by "saltus."$ However, instead of confining our...

A New Proof of E. Cartan's Theorem on the Topology of Semi-simple Groups

GEORGE DANIEL MOSTOW

An Analogue of Hardy’s Theorem for Very Rapidly Decreasing Functions on Semi-simple Lie Groups

A celebrated theorem of L. Schwartz asserts that a function f on R is ‘rapidly decreasing’ (or in the ‘Schwartz class’) iff its Fourier transform is ‘rapidly decreasing’. Since this theorem is of fundamental importance in harmonic analysis, there is a whole body of literature devoted to generalizing this result to other Lie groups. (For example, see [18].) In sharp contrast to Schwartz’s theore...

Rational Points on Compactifications of Semi-simple Groups of Rank

— We explain our approach to the problem of counting rational points of bounded height on equivariant compactifications of semi-simple groups.