Hong oh Kim
Ulsan National Institute of Science and Technology · Mathematics
About the Lab
Professor Hong Oh Kim's research lab specializes in harmonic analysis, wavelet theory, and complex analysis, with a focus on frame multiresolution analyses, refinable functions, and integral operators on the unit disk. The lab investigates semi-orthogonal and frame wavelets, including their construction, regularity, and approximation properties, as well as their connections to dilation matrices and shift-invariant spaces. A significant part of the work involves the analysis of holomorphic functions and their Nevanlinna counting functions, with applications to fractional integrals and function spaces on the polydisc. The lab also explores pseudo-Butterworth refinable functions and their asymptotic behavior, contributing to the theory of wavelet constructions and approximation theory.
Research Overview
Research Output Trend
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Selected Papers
15Proof. Let f e m and f0
We first characterise semi-orthogonal frame wavelets by generalising the characterisation of orthonormal wavelets. We then characterise those semi-orthogonal frame wavelets that are associated with frame multi-resolution analyses. This is a generalisation of a result of Wang and another result of Papadakis. Finally, we illustrate our results by an example.
A multivariate semi-orthogonal frame multiresolution analysis with a general integer dilation matrix and multiple scaling functions is considered. We first derive the formulas of the lengths of the inital (central) shift-invariant space V 0 and the next dilation space V 1 , and, using these formulas, we then address the problem of the number of the elements of a wavelet set, that is, the length of the shift-invariant space W 0 := V 1 ⊖ V 0 . Finally, we show that there does not exist a ‘genuine’
Research Areas
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