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G-frames as Sums of Some g-orthonormal Bases

Abbas Najati|Mohammad Reza Abdollahpour
경북대학교 자연과학대학 수학과|2013.03|Kyungpook Mathematical Journal|제53권 제1호|pp. 135-141

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참고문헌

키워드

g-Bessel sequenceg-frameg-orthonormal basisg-Riesz basis
주제분류수학

초록

In this paper we show that a g-frame for a Hilbert space H can be written as a linear combination of two g-orthonormal bases for H if and only if it is a g-Riesz basis for H. Also, we show that every g-frame for a Hilbert space H is a multiple of a sum of three g-orthonormal bases for H.

Abstract

In this paper we show that a g-frame for a Hilbert space H can be written as a linear combination of two g-orthonormal bases for H if and only if it is a g-Riesz basis for H. Also, we show that every g-frame for a Hilbert space H is a multiple of a sum of three g-orthonormal bases for H.

참고문헌 (10)

  1. P. G. Casazza, "Every frames is a sum of three (but not two) orthonormal bases- and other frame representations", J. Fourier Anal. Appl, 4, pp.727~732 (1998)
  2. P. G. Casazza, "Frames of subspaces", Contemp. Math., 345, pp.87~113 (2004)
  3. O. Christensen, "An Introduction to Frames and Riesz Bases" (2003), Birkh¨auser
  4. O. Christensen, "Oblique dual frames and shift invariant-spaces", Appl. Comput. Harmon. Anal., 17, pp.48~68 (2004)
  5. R. J. Duffin, "A class of nonharmonic Fourier series", Trans. Amer. Math. Soc., 72, pp.341~366 (1952)
  6. M. Fornasier, "Decompositions of Hibert space: local construction of global frames", Proc. Int. Conf. On Constructive Function Theory, pp.275~281 (2003)
  7. S. Li, "Pseudoframes for subspaces with applications", J. Fourier Anal. Appl., 10, pp.409~431 (2004)
  8. A. Najati, "G-frames and stability of g-frames in Hilbert spaces", Methods Funct. Anal. Topology, 4, pp.271~286 (2008)
  9. S. Obeidat, "Sums of Hilbert Space frames", J. Math. Anal. Appl., 351, pp.579~585 (2009)
  10. W. Sun, "G-frames and g-Riesz bases", J. Math. Anal. Appl., 322, pp.437~452 (2006)

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