In this chapter we survey several recent results on the existence of frames with prescribed norms and frame operator. These results are equivalent to Schur-Horn type theorems which describe possible diagonals of positive self-adjoint operators with specified spectral properties. The first infinite dimensional result of this type is due to Kadison who characterized diagonals of orthogonal projec...

In this paper, we introduce $(mathcal{C},mathcal{C}')$-controlled continuous $g$-Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frames is a $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frame. Also, we investigate when a $(mathcal{C},mathca...

We investigate the stability properties of strongly continuous semigroups generated by operators form $A-BB^\ast$, where $A$ is a generator contraction semigroup and $B$ possibly unbounded operator. Such systems arise naturally in study hyperbolic partial differential equations with damping on boundary or inside spatial domain. As our main results we present general sufficient conditions for no...

Assumptions Intermediate language: RISC-like 3-address code‡ Intermediate Code Generation (ICG) is independent of target ISA Storage layout has been pre-determined Infinite number of registers + Frame Pointer (FP) Q. What values can live in registers? ‡ ILOC: Cooper and Torczon, Appendix A. Strategy 1. Simple bottom-up tree-walk on AST 2. Translation uses only local info: current AST node + chi...

Abstract. The construction of frames for a Hilbert space H can be equated to the decomposition of the frame operator as a sum of positive operators having rank one. This realization provides a different approach to questions regarding frames with particular properties and motivates our results. We find a necessary and sufficient condition under which any positive finite-rank operator B can be e...

Let H be a separable Hilbert space, let G ⊂ H, and let A be an operator on H. Under appropriate conditions on A andG, it is known that the set of iterations FG(A) = {Ag | g ∈ G, 0 ≤ j ≤ L(g)} is a frame for H. We call FG(A) a dynamical frame for H, and explore further its properties; in particular, we show that the canonical dual frame of FG(A) also has an iterative set structure. We explore th...

and concrete syntax for infix operators Type rator represents a binary infix operator, which has a text representation, a precedence, and an associativity: hinfixi type precedence = int datatype associativity = LEFT | RIGHT | NONASSOC type rator = string * precedence * associativity This ML code uses simple integers (int) to represent precedence, an enumeration to represent associativity, and a...

for all x∈H . When A = B the frame is said to be tight and if in addition, A = B = 1 it is termed a Parseval frame. When F = { fi}i=1 is a frame, we shall abuse notations and denote by F again, the n×M matrix whose ith column is fi, and where n is the dimension of H . Using this notation, the frame operator is the n×n matrix S=FF∗ where F∗ is the adjoint of F . It is a folklore to note that F i...