GENERALIZED SHIFT-INVARIANT SYSTEMS AND DUAL FRAMES FOR SUBSPACES

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GHOLAMI N.

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Seminar Paper

Paper Information

Seminar: SEMINAR ON HARMONIC ANALYSIS AND APPLICATIONS
Year:2017 | Issue:5

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Information Seminar Paper

Title

GENERALIZED SHIFT-INVARIANT SYSTEMS AND DUAL FRAMES FOR SUBSPACES

Author(s)

GHOLAMI N.

Keywords

FRAMES FOR SUBSPACES

GENERALIZED SHIFT-INVARIANT SYSTEMS

APPROXIMATELY DUAL FRAMES

Abstract

LET TK DENOTE TRANSLATION BY KÎZD . GIVEN COUNTABLE COLLECTIONS OF FUNCTIONS (FORMULA) AND ASSUMING THAT (FORMULA) ARE BESSEL SEQUENCES, WE ARE INTERESTED IN EXPANSIONS (FORMULA) OUR MAIN RESULT GIVES AN EQUIVALENT CONDITION FOR THIS TO HOLD IN A MORE GENERAL SETTING THAN DESCRIBED HERE, WHERE TRANSLATION BY K ÎZD IS REPLACED BY TRANSLATION VIA THE ACTION OF A MATRIX. AS SPECIAL CASES OF OUR RESULT WE FIND CONDITIONS FOR SHIFT-INVARIANT SYSTEMS TO GENERATE A SUBSPACE FRAME WITH A CORRESPONDING DUAL HAVING THE SAME STRUCTURE. IN THIS PAPER WE CONSIDER THE IMPORTANT CASE OF GENERALIZED SHIFT-INVARIANT SYSTEMS AND PROVIDE VARIOUS WAYS OF ESTIMATING THE DEVIATION FROM PERFECT RECONSTRUCTION THAT OCCUR WHEN THE SYSTEMS DO NOT FORM DUAL FRAMES. THE DEVIATION FROM BEING DUAL FRAMES WILL BE MEASURED EITHER IN TERMS OF A PERTURBATION CONDITION OR IN TERMS OF THE DEVIATION FROM EQUALITY IN THE DUALITY CONDITIONS.

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APA: Copy

GHOLAMI, N.. (2017). GENERALIZED SHIFT-INVARIANT SYSTEMS AND DUAL FRAMES FOR SUBSPACES. SEMINAR ON HARMONIC ANALYSIS AND APPLICATIONS. SID. https://sid.ir/paper/940046/en

Vancouver: Copy

GHOLAMI N.. GENERALIZED SHIFT-INVARIANT SYSTEMS AND DUAL FRAMES FOR SUBSPACES. 2017. Available from: https://sid.ir/paper/940046/en

IEEE: Copy

N. GHOLAMI, “GENERALIZED SHIFT-INVARIANT SYSTEMS AND DUAL FRAMES FOR SUBSPACES,” presented at the SEMINAR ON HARMONIC ANALYSIS AND APPLICATIONS. 2017, [Online]. Available: https://sid.ir/paper/940046/en

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