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Digitale Medien

Affine frames, quasi-affine frames, and their duals (1998)

Chui, Charles K. ; Shi, Xianliang ; Stöckler, Joachim

Springer

Advances in computational mathematics 8 (1998), S. 1-17

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Details

ISSN: 1572-9044

Schlagwort(e): affine frame ; quasi-affine frame ; dual ; sesquilinear operator ; translation invariance ; 42C15 (primary) ; 42B15 ; 47N40 (secondary)

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract The notion of quasi-affine frame was recently introduced by Ron and Shen [9] in order to achieve shift-invariance of the discrete wavelet transform. In this paper, we establish a duality-preservation theorem for quasi-affine frames. Furthermore, the preservation of frame bounds when changing an affine frame to a quasi-affine frame is shown to hold without the decay assumptions in [9]. Our consideration leads naturally to the study of certain sesquilinear operators which are defined by two affine systems. The translation-invariance of such operators is characterized in terms of certain intrinsic properties of the two affine systems.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1023/A:1018975725857

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