• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.753-762
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• 2012

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane. We also prove new analogous results in the context of bounded strictly pseudoconvex domains with smooth boundary.

• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.269-284
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• 2000

We discuss completeness with respect to the Caratheodory distance, the Kobayashi distance and the Beraman distance, respectively.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.85-103
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• 2015

We prove some sharp extremal distance results for functions in various spaces of analytic functions on bounded strictly pseudoconvex domains with smooth boundary. Also, we obtain atomic decompositions in multifunctional Bloch and weighted Bergman spaces of analytic functions on strictly pseudoconvex domains with smooth boundary, which extend known results in the classical case of a single function.

• Journal of Information Processing Systems
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• v.16 no.1
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• pp.30-41
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• 2020

Lines and textures are natural properties of the surface of natural objects, and their images can be sparsely represented in suitable frames such as wavelets, curvelets and wave atoms. Based on characteristics that the curvelets framework is good at expressing the line feature and wavesat is good at representing texture features, we propose a model for the weighted sparsity constraints of the two frames. Furtherly, a multi-step iterative fast algorithm for solving the model is also proposed based on the split Bergman method. By introducing auxiliary variables and the Bergman distance, the original problem is transformed into an iterative solution of two simple sub-problems, which greatly reduces the computational complexity. Experiments using standard images show that the split-based Bergman iterative algorithm in hybrid domain defeats the traditional Wavelets framework or curvelets framework both in terms of timeliness and recovery accuracy, which demonstrates the validity of the model and algorithm in this paper.