G-Frames, g-orthonormal bases and g-Riesz bases
الموضوعات :
1 - Department of Mathematics, Faculty of Science, Islamic Azad University,
Central Tehran Branch, Tehran, Iran
الکلمات المفتاحية: G-frames, G-Bessel sequences, G-orthonormal bases,
ملخص المقالة :
G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection betweeng-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its de nes a boundedoperator.
[1] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, Boston, (2003).
[2] I. Daubechies, A. Grossmann and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys. 27(1986), 1271-1283.
[3] R. J. Duffin and A. C. Schae er, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72,(2), (1952), 341-366.
[4] M. Fornasier, Quasi-orthogonal decompositions of structured frames, J. Math. Anal. Appl. 289 (2004), 180-199.
[5] D. Gabor, Theory of communications, J. Inst. Electr. Eg. London. 93(III), (1946), 429-457.
[6] W. Sun, G-frames and G-Riesz bases, J. Math. Anal. Appl. (2006), 322, 437-452.
[7] R. Young, An Introduction to Nonharmonic Fourier Series, Academic Press, New York, (2001).
