Applications of Invariant Differential Operators to Multivariate Distribution Theory
نویسندگان
چکیده
منابع مشابه
Of Invariant Differential Operators to Multivariate Distribution Theory
The invariant differential operators are applied to derive partial differential equations for the zonal polynomials, to the calculation of generalized binomial coefficients and certain multivariate integrals, and to deducing a characterization of EP functions (Kushner, Lebow and Meisner, J. MUltivariate Anal., 1981).
متن کاملInvariant Theory and Differential Operators
Constructive invariant theory was a preoccupation of many nineteenth century mathematicians, but the topic fell out of fashion in the early twentieth century. In the latter twentieth century the topic enjoyed a resurgence, partly due to its connections with the construction of moduli spaces in algebraic geometry and partly due to the development of computational algorithms suitable for implemen...
متن کاملInvariant differential operators
on the complex upper half-plane H, provably invariant under the linear fractional action of SL2(R), but it is oppressive to verify this directly. Worse, the goal is not merely to verify an expression presented as a deus ex machina, but, rather to systematically generate suitable expressions. An important part of this intention is understanding reasons for the existence of invariant operators, a...
متن کاملInvariant Differential Operators On
For two positive integers m and n, we let Pn be the open convex cone in R consisting of positive definite n × n real symmetric matrices and let R be the set of all m×n real matrices. In this article, we investigate differential operators on the non-reductive manifold Pn × R (m,n) that are invariant under the natural action of the semidirect product group GL(n,R)⋉R on the MinkowskiEuclid space P...
متن کاملDimensional Reduction of Invariant Fields and Differential Operators. II. Reduction of Invariant Differential Operators
In the present paper, which is a sequel of [1], we consider the dimensional reduction of differential operators (DOs) that are invariant with respect to the action of a connected Lie group G. The action of G on vector bundles induces naturally actions of G on their sections and on the DOs between them. In [1] we constructed explicitly the reduced bundle ξ, such that the set of all its sections,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Applied Mathematics
سال: 1985
ISSN: 0036-1399,1095-712X
DOI: 10.1137/0145015