Rational approximation to values of G-functions, and their expansions in integer bases

Short rational generating functions and their applications to integer programming

In this paper, we provide an overview of rational generating function tools for encoding integer points inside a rational polyhedron, and we examine their applications to solving integer programming problems.

Topological Approximation and Compression of Functions and Their Wavelet Expansions

G-Frames, g-orthonormal bases and g-Riesz bases

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

Greedy and Quasi-greedy Expansions in Non-integer Bases

We generalize several theorems of Rényi, Parry, Daróczy and Kátai by characterizing the greedy and quasi-greedy expansions in non-integer bases.

Expansions in Non-integer Bases: Lower, Middle and Top Order

Let q ∈ (1, 2); it is known that each x ∈ [0, 1/(q− 1)] has an expansion of the form x = ∑ ∞ n=1 anq −n with an ∈ {0, 1}. It was shown in [3] that if q < ( √ 5 + 1)/2, then each x ∈ (0, 1/(q − 1)) has a continuum of such expansions; however, if q > ( √ 5 + 1)/2, then there exist infinitely many x having a unique expansion [4]. In the present paper we begin the study of parameters q for which th...