For a connected linear semisimple Lie group , this paper considers those nonzero limits of discrete series representations having infinitesimal character 0, calling them totally degenerate. Such representations exist if and only if has a compact Cartan subgroup, is quasisplit, and is acceptable in the sense of Harish-Chandra.
Totally degenerate limits of discrete series are natural objects of study in the theory of automorphic forms: in fact, those automorphic representations of adelic groups that have totally degenerate limits of discrete series as archimedean components correspond conjecturally to complex continuous representations of Galois groups of number fields. The automorphic representations in question have important arithmetic significance, but very little has been proved up to now toward establishing this part of the Langlands conjectures.
There is some hope of making progress in this area, and for that one needs to know in detail the representations of under consideration. The aim of this paper is to determine the classification parameters of all totally degenerate limits of discrete series in the Knapp-Zuckerman classification of irreducible tempered representations, i.e., to express these representations as induced representations with nondegenerate data.
The paper uses a general argument, based on the finite abelian reducibility group attached to a specific unitary principal series representation of . First an easy result gives the aggregate of the classification parameters. Then a harder result uses the easy result to match the classification parameters with the representations of under consideration in representation-by-representation fashion. The paper includes tables of the classification parameters for all such groups .
In this paper I consider a class of non-standard singular integrals motivated by potential theoretic and probabilistic considerations.
The probabilistic applications, which are by far the most interesting part of this circle of ideas, are only outlined in Section
1.5: They give the best approximation of the solution of the classical Dirichlet problem in a Lipschitz domain by the corresponding solution by finite differences.
The potential theoretic estimate needed for this gives rise to a natural duality between the Lp functions on the boundary ∂Ω and a class of functions A on Ω that was first considered by Dahlberg. The actual duality is given by ∫Ω S f(x)A(x)dx = (f, A) where S f(x) = ∫∂Ω |x − y|1−nf(y)dy is the Newtonian potential.
We can identify the upper half Lipschitz space with in the obvious way and express for an appropriate kernel K. It is the boundedness properties of the above (for , ) that is the essential part of this work. This relates with more classical (but still “rough”) singular integrals that have
been considered by Christ and Journé.
Lecture held in the Seminario Matematico e Fisico on March 14, 2005
Received: April 2007 相似文献
In this paper,the functions of warping displacement interruption defined on the crack lines are taken for the fundamental unknown functions.The torsion problem of cracked circular cylinder is reduced to solving a system of integral equations with strongly singular kernels.Using the numerical method of these equations,the torsional rigidities and the stress intensity factors are calculated to solve the torsion problem of circular cylinder with star-type and other different types of cracks.The numerical results are satisfactory. 相似文献
Using a singular perturbation method,the nonlinear stability of a truncated shallow,spherical shell without a nondeformable rigid body at the center under linear distributed loads along the interior edge is investigated in this paper.When the geometrical parameter k is large,the uniformly valid asymptotic solutions are obtained. 相似文献
In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with
the character of detected phase being g(φ)=(1+k)sinφ/1+kcosφ. 相似文献
In this paper,we consider the vector nonlinear boundary value problem:εy~v=f(x,y,z,y′,ε),y(0)=A_1,y(1)=B_1εz~v=g(x,y,z,z′,ε),z(0)=A_2,z(1)=B_2whereε>0 is a small parameter,0≤x≤1 ,f and g are continuous functions in R~4,Under appropriate assumptions,by means of the differential inequalities,we demonstratethe existence and estimation,involving boundary and interior layers,of the solutions to theabove problem. 相似文献