Polynomial spaces reproduced by elliptic scaling functions

Polynomial Approximation of Functions in Sobolev Spaces

Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hubert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer o...

Theta Functions, Elliptic Hypergeometric Series, and Kawanaka’s Macdonald Polynomial Conjecture

We give a new theta-function identity, a special case of which is utilised to prove Kawanaka’s Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which appears to be new even in the one-variable, basic case.

Testing Polynomial Equivalence by Scaling Matrices

Polynomial estimates for c-functions on reductive symmetric spaces

The c-functions, related to a reductive symmetric space G/H and a fixed representation τ of a maximal compact subgroup K of G, are shown to satisfy polynomial bounds in imaginary directions.

Function spaces vs. Scaling functions: Some issues in image classification

Criteria based on the computation of fractal dimensions have been used in order to perform image analysis and classification; we show that such criteria often amount to determine the regularity of the image in some classes of function spaces, and that looking for richer criteria naturally leads to the introduction of new classes of function spaces. We will investigate the properties of some of ...