Hong Oh Kim
Korea Advanced Institute of Science and Technology · Mathematics
About the Lab
Professor Hong Oh Kim's research lab specializes in complex analysis, harmonic analysis, and wavelet theory, with a focus on Hardy spaces, plurisubharmonic functions, and multiresolution analyses. The lab investigates the interplay between function spaces, maximal functions, and operator invariance in the unit ball and complex domains, particularly in relation to $ L^p $-norm estimates and radial maximal functions. A significant part of the work involves characterizing holomorphic functions and frame multiresolution analyses with general dilation matrices and multiple scaling functions. The lab also explores coefficient estimates and embedding theorems in Hardy spaces, often in collaboration with leading analysts in the field.
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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