Results 1 
4 of
4
Radiation fields, scattering and inverse scattering on asymptotically hyperbolic manifolds
, 2004
"... ..."
A local Weyl’s law, the angular distribution and multiplicity of cusp forms on product spaces
 Trans. of American Math. Society
"... Abstract. Let Y\ßf be a finite volume symmetric space with %? the product of half planes. Let A, be the Laplacian on the ¡th half plane, and assume that we have a cusp form , so we have A, = X¡ for i = 1, 2,..., n. Let A = (Ai,..., An) and let with rj + j = A,. Letting r = (ri.rn), R = \/> ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Abstract. Let Y\ßf be a finite volume symmetric space with %? the product of half planes. Let A, be the Laplacian on the ¡th half plane, and assume that we have a cusp form <f>, so we have A,</> = X¡<f> for i = 1, 2,..., n. Let A = (Ai,..., An) and let with rj + j = A,. Letting r = (ri.rn), R = \/> \ + ■ ■ ■ + r2„ we let M(r) denote the dimension of the space of cusp forms with eigenvalue A. More generally, let M(r, a) denote the number of independent eigenfunctions such that the r associated to an eigenfunction is inside the ball of radius a, centered at f. We will define a function f(r), which is generally equal to a linear sum of products of the r¡. We prove the following theorems.
A Note On Some Positivity Conditions Related To Zeta And LFunctions
 IMRN
, 1998
"... Introduction The theory of Hilbert spaces of entire functions [1] was developed by Louis de Branges in the late 1950s and early 1960s with the help of his students including James Rovnyak and David Trutt. It is a generalization of the part of Fourier analysis involving Fourier transform and Plancher ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Introduction The theory of Hilbert spaces of entire functions [1] was developed by Louis de Branges in the late 1950s and early 1960s with the help of his students including James Rovnyak and David Trutt. It is a generalization of the part of Fourier analysis involving Fourier transform and Plancherel formula. The de BrangesRovnyak theory of square summable power series, whichplayed an important role in leading to de Branges' discovery of a proof of the Bieberbach conjecture, originated from the theory of Hilbert spaces of entire functions. In [2] de Branges proposed an approach to the generalized Riemann hypothesis, that is, the hypothesis that not only the Riemann zeta function i(s) but also all the Dirichlet Lfunctions L(s# ) with primitive have their nontrivial zeros lying on the critical line !s = 1=2 (See Davenport [5]). In [2] de Br
SPECTRAL MULTIPLICITY FOR Gln(R)
"... Abstract. We study the behavior of the cuspidal spectrum of T\^, where %? is associated to Gln(i?) and V is cofinite but not compact. By a technique that modifies the LaxPhillips technique and uses ideas from wave equation techniques, if r is the dimension of JP, Na{k) is the counting function for ..."
Abstract
 Add to MetaCart
Abstract. We study the behavior of the cuspidal spectrum of T\^, where %? is associated to Gln(i?) and V is cofinite but not compact. By a technique that modifies the LaxPhillips technique and uses ideas from wave equation techniques, if r is the dimension of JP, Na{k) is the counting function for the Laplacian attached to a Hilbert space Ha, Ma(X) is the multiplicity function, and Ho is the space of cusp forms, we obtain the following results: Theorem 1. There exists a space of functions // ' , containing all cusp forms, such that