This collection of lecture notes is based on a series of lectures presented by the authors at
the Institute for Advanced Studies/Park City Mathematics 2010 Summer Program on “The …

In this paper, we introduce complex pseudo splines that are derived from pseudo splines of
type I. First, we show that the shifts of every complex pseudo spline are linearly independent …

Dual pseudo splines constitute a new class of refinable functions with B-splines as special
examples. In this paper, we shall construct Riesz wavelet associated with dual pseudo …

In this paper, we introduce the concept of d-dilation (dual) pseudo-splines in L 2 (ℝ) with
dilation d≥ 2, characterize the linear independence of the integer shifts, the subdivision …

Let $ d\geq 1$ be a natural number and $ A_0 $ be a $ d\times d $ expansive integral matrix
with determinant $\pm 2. $ Then $ A_0 $ is integrally similar to an integral matrix $ A $ with …