In this study, we establish a Parseval equality and an expansion formula for a Sturm– Liouville operator on semi-unbounded time scales. AMS subject classification: 34L10.

A generalized continuous frame is a family of operators on a Hilbert space H which allows reproductions of arbitrary elements of H by continuous superpositions. Generalized continuous frames are natural generalization of continuous and discrete frames in Hilbert spaces which include many recent generalization of frames. In this article,we associate to a generalized continuous frame suitable Ban...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions on $L$. We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n}) mbox{ is a compact frame for any $n in mathbb{N}$}}.$$ Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the set ${x in X: |f(x)|geq dfrac{1...

The theory of c-frames and c-Bessel mappings are the generalizationsof the theory of frames and Bessel sequences. In this paper, weobtain several equivalent conditions for dual of c-Bessel mappings.We show that for a c-Bessel mapping $f$, a retrievalformula with respect to a c-Bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-Besselmapping which  wea...

We present a set of functions in L2([0,∞)) and show it to be a (tight) generalized frame (as presented by G. Kaiser (1994)). The analysis side of the frame operation is called the continuous unified transform. We show that some of the well-known transforms (such as Laplace, Laguerre, Kautz, and Hambo) result by creating different sampling patterns in the transform domain (or, equivalently, choo...

Time framing strategies such as Stop-and-Go (S&G) [Golestani S.J., Congestion-free transmission of real-time traffic of real-time traffic in packet networks, IEEE INFOCOM, 1990, pp.527-536; Golestani S.J., A framing strategy for congestion management, IEEE JSAC, 9(7), 1991, pp.1064-1077; Golestani S.J., Congestion-free communication in high-speed packet networks, IEEE Trans. on Communications, ...