𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Frame Approximation of Pseudo-Inverse Operators

✍ Scribed by Ole Christensen

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
86 KB
Volume
261
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

Let T denote an operator on a Hilbert space β€’ β€’ , and let f i ∞ i=1 be a frame for the orthogonal complement of the kernel N T . We construct a sequence of operators n of the form n β€’ = n i=1 β€’ g n i f i which converges to the psuedoinverse T † of T in the strong operator topology as n β†’ ∞. The operators n can be found using finite-dimensional methods. We also prove an adaptive iterative version of the result.

πŸ“œ SIMILAR VOLUMES

Frames and Pseudo-Inverses
Frames and Pseudo-Inverses
✍ O. Christensen πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 407 KB
The Inverse Laplace Transform and Analyt
The Inverse Laplace Transform and Analytic Pseudo-Differential Operators
✍ A. Boumenir; A. Al-Shuaibi πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 130 KB

By comparing the Laplace transform L L with the differential operator D, we y1 Ε½ . y1 Ε½ . obtain a formula for the inverse Laplace transform L L s 1r V cos D VL L , where V is a unitary transformation operator. This helps us obtain an explicit spectral representation of L L. Some applications of the

Pseudo-Duals of Frames with Applications
Pseudo-Duals of Frames with Applications
✍ Shidong Li; Hidemitsu Ogawa πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 155 KB

We show that there are duals {x \* n } to a given (nonexact) frame {x n } that are not usual frames. In particular, these duals are not Bessel sequences. We call them pseudo-duals. A characterization and a constructions of pseudo-duals are given. Examples and potential applications of pseudo-dual th