Write E for the stable discrete series character associated to an irreducible nite-dimensional representation E of a connected real reductive group G. Let M be the centralizer of the split component of a maximal torus T , and denote by M ( ; E) Arthur's extension of jDG M ( )j 12 E( ) to T (R). In this paper we give a simple explicit expression for M ( ; E), when is elliptic in G. We do not ass...

We deal with the smoothed estimators for conditional probability functions of discrete-valued time series fY t g under two diierent settings. When the conditional distribution of Y t given its lagged values falls in a parametric family and depends on exogenous random variables, a smoothed maximum (partial) likelihood estimator for the unknown parameter is proposed. While there is no prior infor...

We give a brief review of some of the wavelet-based techniques currently available for the analysis of arbitrary-length discrete time series. We discuss the maximal overlap discrete wavelet packet transform (MODWPT), a non-decimated version of the usual discrete wavelet packet transform, and a special case, the maximal overlap discrete wavelet transform (MODWT). Using least-asymmetric or coifle...

We now start considering discrete–time signals. A discrete–time signal is a function (real or complex valued) whose argument runs over the integers, rather than over the real line. We shall use square brackets, as in x[n], for discrete–time signals and round parentheses, as in x(t), for continuous–time signals. This is the notation used in EECE 359 and EECE 369. Discrete–time signals arise in t...

In this paper the analytic continuation of the holomorphic discrete series is defined. The most elementary properties of these representations are developed. The study of when these representations are unitary is begun.

The decomposition of the tensor product of a positive and a negative discrete series representation of the Lie algebra su(1, 1) is a direct integral over the principal unitary series representations. In the decomposition discrete terms can occur, and the discrete terms are a finite number of discrete series representations or one complementary series representation. The interpretation of Meixne...

The tensor product of a positive and a negative discrete series representation of the quantum algebra Uq ( su(1, 1) ) decomposes as a direct integral over the principal unitary series representations. Discrete terms can appear, and these terms are a finite number of discrete series representations, or one complementary series representation. From the interpretation as overlap coefficients of li...

Due to developments in additive manufacturing, the production of piezoelectric materials with complex geometries is becoming viable and enabling the manufacturing of thicker harvesters. Therefore, in this study a piezoelectric harvesting device is modelled as a bimorph cantilever beam with a series connection and an intermediate metallic substrate using the plain strain hypothesis. On the other...