Let [Formula: see text] be a congruence subgroup of text]. Using Poincaré series text]-finite matrix coefficients integrable discrete representations text], we construct spanning set for the space Siegel cusp forms weight We prove non-vanishing certain elements this using Muić’s integral criterion on locally compact Hausdorff groups. Moreover, representation theory study Petersson inner product...

Many popular probabilistic models for temporal sequences assume simple hidden dynamics or low dimensionality of discrete variables. For higher dimensional discrete hidden variables, recourse is often made to approximate mean field theories, which to date have been applied to models with only simple hidden unit dynamics. We consider a class of models in which the discrete hidden space is defined...

The main aim of this paper is the development of suitable bases (replacing the power basis x (n ∈ N≥0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms...

In this work we generalize the non-parametric quasi-likelihood method to the context of discrete choice models for time series data and, in particular, when lags of the discrete dependent variable appear among regressors. We derive consistency and asymptotic normality of the estimator for such models for general case and present an application to real data on US recessions.