The Newton Polyhedron and Positivity of $${}_2F_3$$ Hypergeometric Functions

Total Positivity Properties of Generalized Hypergeometric Functions of Matrix Argument

In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized (0F1) hypergeometric function of two real symmetric matrix arguments. In this paper, we make use of zonal polynomial expansions to obtain a new proof of a result that these 0F1 functions fail to satisfy certain pairwise total positivity properties; this proof extends both to arb...

Integral Properties of Zonal Spherical Functions, Hypergeometric Functions and Invariant

Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.

A Subclass of Analytic Functions Associated with Hypergeometric Functions

In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.

Maximal averages over hypersurfaces and the Newton polyhedron

Here φ(x) is a smooth cutoff function that localizes the surface S near some specific y ∈ S. The goal here is to determine the values of p for which M is bounded on L. The earliest work on this subject was done in the case where S is a sphere, when Stein [St1] showed M is bounded on L iff p > n+1 n for n > 1. This was later generalized by Greenleaf [Gr] to surfaces of nonvanishing Gaussian curv...

Hypergeometric Functions