Frames and semi-frames
Abstract
Loosely speaking, a semi-frame is a generalized frame for which one of the frame bounds is absent. More precisely, given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded inverse, whereas a lower semi-frame has an unbounded frame operator, with a bounded inverse. We study mostly upper semi-frames, both in the continuous and discrete case, and give some remarks for the dual situation. In particular, we show that reconstruction is still possible in certain cases.
- Publication:
-
Journal of Physics A Mathematical General
- Pub Date:
- May 2011
- DOI:
- 10.1088/1751-8113/44/20/205201
- arXiv:
- arXiv:1101.2859
- Bibcode:
- 2011JPhA...44t5201A
- Keywords:
-
- Mathematics - Functional Analysis;
- Mathematical Physics;
- 42C15;
- 42C40;
- 65T60
- E-Print:
- 25 pages