Matrices defined by frames

• Autorzy: Ambroziński Z. , Rudol K.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

frames; operators; spectrum

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2009
• Tom: Vol. 29, no. 4
• Strony: 365--375
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Ambroziński Z.

autor

Rudol K.

• AGH University of Science and Technology, Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Cracow, Poland,

Bibliografia

• [1] Z. Ambroziński, Commutation Relations for some quantum mechanics operators and their models, M. Sci. Thesis AGH, Krakow, 2009 [in Polish].
• [2] P. Balazs, Matrix representation of operators using frames, Sampling Theory in Signal Image Processing 7 (2008) 1, 39–54.
• [3] P. Balazs, Basic definitions and properties of Bessel multipliers, J. Math. Anal. Appl. 325 (2007), 571–585.
• [4] J. Bergh, J. Löfström, Interpolation Spaces. An Introduction, Springer-Verlag, Berlin, 1976.
• [5] P.G. Casazza, The art of frame theory, Taiwanese J. Math. 2 (2000) 4, 129–202.
• [6] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhäuser, Boston, Basel, Berlin, 2003.
• [7] H.G. Feichtinger, K.H. Gröchenig, Banach spaces related to integrable group representations and their atomic decomposition I, J. Funct. Anal. 86 (1989), 307–340.
• [8] S. Mallat, A wavelet Tour of Signal Processing, Academic Press, San Diego, 1999.
• [9] K. Rudol, Atomic-type decompositions in the Segal-Bargmann space, Proc. Roy. Irish Acad. 88 A (1988), 85–90.