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Featured researches published by Yoo Young Koo.


Numerical Functional Analysis and Optimization | 2013

Applications of Parameterizations of Oblique Duals of a Frame Sequence

Hyoung Seok Kim; Yoo Young Koo; Jae Kun Lim

Two parameterizations of oblique duals of a given frame sequence are applied to show that the sum of a frame sequence and one of its oblique duals may not be a frame sequence, and that type II dual is locally (and globally) optimal in some sense and that the excesses of the frame sequence and its oblique duals are the same. Other observations on the duals of a frame sequence are included also.


Linear & Multilinear Algebra | 2013

Sum and direct sum of frame sequences

Yoo Young Koo; Jae Kun Lim

Casazza, Han and Larson characterized various properties of the direct sum of two frame sequences. We add characterizations of other properties and study the relationship between the direct sum and the sum of frame sequences. In particular, we find a necessary and sufficient condition for the sum of two strongly disjoint (orthogonal) frame sequences (in the same Hilbert space) to be a frame sequence, and thereby show that the sum of two strongly disjoint frame sequences may not be a frame sequence. We also show that the closedness of the sum of the synthesis operators of two frame sequences and that of the sum of the frame operators of the same frame sequences are not related. Other observations are also included.


Quaestiones Mathematicae | 2011

Schatten-Class operators and frames

Yoo Young Koo; Jae Kun Lim

By extending the works of Arias et al. and Balazs we present a natural sufficient condition via frames for the membership of the Schatten p-class operators for 1 ≤ p ≤ 2, and show that such a condition is not sufficient to guarantee the membership of the Schatten-class operators for p > 2.By extending the works of Arias et al. and Balazs we present a natural sufficient condition via frames for the membership of the Schatten p-class operators for 1 ≤ p ≤ 2, and show that such a condition is not sufficient to guarantee the membership of the Schatten-class operators for p > 2. Quaestiones Mathematicae 34(2011), 203–211.


Proceedings of SPIE | 2009

Duals and invariances of frame sequences

Shannon Bishop; Christopher Heil; Yoo Young Koo; Jae Kun Lim

This paper surveys recent results on frame sequences. The first group of results characterizes the relationships that hold among various types of dual frame sequences. The second group of results characterizes the relationships that hold among the major Paley-Wiener perturbation theorems for frame sequences, and some of the properties that remain invariant under such perturbations.


Linear & Multilinear Algebra | 2008

Finite orthogonal frames generated by normal operators

Yoo Young Koo; Jae Kun Lim; In-Sook Shin

We first characterize finite frames and orthogonal frames generated by normal operators on , and apply the results to (orthogonal) generalized harmonic frames. We also show that the canonical dual frame of a finite frame generated by a normal operator on is always generated by a (not-necessarily normal) operator, and give a condition when a finite frame generated by a normal operator has an alternate dual frame generated by a normal operator.


Acta Applicandae Mathematicae | 2009

Duals of Frame Sequences

Christopher Heil; Yoo Young Koo; Jae Kun Lim


Linear Algebra and its Applications | 2007

Perturbation of frame sequences and its applications to shift-invariant spaces☆

Yoo Young Koo; Jae Kun Lim


Linear Algebra and its Applications | 2010

Invariances of Frame Sequences under Perturbations

Shannon Bishop; Christopher Heil; Yoo Young Koo; Jae Kun Lim


Bulletin of the Malaysian Mathematical Sciences Society | 2018

Sum of Disjoint Frame Sequences

Yoo Young Koo; Jae Kun Lim


Electronic Journal of Linear Algebra | 2015

Extension of Bessel sequences to oblique dual frame sequences and the minimal projection

Yoo Young Koo; Jae Kun Lim

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Jae Kun Lim

Hankyong National University

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Christopher Heil

Georgia Institute of Technology

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Shannon Bishop

Georgia Institute of Technology

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