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Lower Semi-frames, Frames, and Metric Operators
- Source :
- Mediterranean Journal of Mathematics. 18
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive self-adjoint operator. A necessary condition is that the domain of the analysis operator associated with the function be dense. The study is done also with the help of the generalized frame operator associated with a weakly measurable function, which has better properties than the usual frame operator. A special attention is given to lower semi-frames: indeed, if the domain of the analysis operator is dense, then a lower semi-frame can be transformed into a Parseval frame with a (special) metric operator.
- Subjects :
- Pure mathematics
General Mathematics
010102 general mathematics
Frame (networking)
Hilbert space
lower semi-frames
Weakly measurable function
Function (mathematics)
01 natural sciences
Domain (mathematical analysis)
Parseval's theorem
Frames
symbols.namesake
Operator (computer programming)
Settore MAT/05 - Analisi Matematica
0103 physical sciences
Metric (mathematics)
symbols
metric operators
0101 mathematics
010306 general physics
Mathematics
Subjects
Details
- ISSN :
- 16605454 and 16605446
- Volume :
- 18
- Database :
- OpenAIRE
- Journal :
- Mediterranean Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....fb1630985fb141c51e204d8fb4e7c0e0