Matrices defined by frames - Ambroziński, Zbigniew; Rudol, Krzysztof (My University, 2009)
Matrix representations of bounded Hilbert space operators are considered. The matrices in question are defined with respect to frames, rather than bases. The frames, a generalisation of bases, used extensively in applied harmonic analysis, are overcomplete sequences. We consider some properties related to tight frames, where, up to some multiplicative constant, a form of Parseval Identity takes place. We also describe parts of spectra of operators in terms of their matrices.
Opuscula Mathematica
Keywords: frames; operators; spectrum