• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2013-2027
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• 2017

We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.259-269
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• 2006

We obtain a characterization of commuting Toeplitz operators with holomorphic symbols acting on the pluriharmonic Bergman space of the polydisk. We also obtain a characterization of normal Toeplitz operators with pluriharmonic symbols. In addition, some results for special types of semi-commutators are included.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.621-642
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• 2009

In this paper we give necessary and sufficient conditions that two Toeplitz operators with monomial symbols acting on the weighted Bergman space commute. We also present necessary and sufficient conditions for the hyponormality of Toeplitz operators with some special symbols on the weighted Bergman space. All the results are stated in terms of the Mellin transform of the symbol.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.155-162
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• 2018

In this paper, we are concerned with hyponormal Toeplitz operators on the Hardy space of the unit circle. Our main result of this paper is to provide a simple and transparent proof on the hyponormality of Toeplitz operators with symmetric-type symbols via Schur complement lemma.

• East Asian mathematical journal
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• v.40 no.1
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• pp.95-107
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• 2024

Let K be an imaginary quadratic field with ring of integers 𝓞_K and N be a positive integer. By K_(N) we mean the ray class field of K modulo N𝓞_K. In this paper, for each prime p of K relatively prime to N𝓞_K we explicitly describe the action of the Artin symbol (${\frac{K_{(N)}/K}{p}}$) on special values of modular functions of level N. Furthermore, we extend the Kronecker congruence relation for the elliptic modular function j to some modular functions of higher level.

• 한국게임학회지
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• v.8 no.1
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• pp.32-38
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• 2011

The help or guide sentences of educational math games which use mathematical statements need to represent graphical forms for the learners of the game generation whose cognitive style is graphic first. In this paper, we proposed an object-based visual representation method for mathematical statements. It has object-based description rules to use graphical symbols and mathematical symbols with text words. It is easy to describe or to understand accurately mathematical meaning and is also fast for learners to read for understanding. The proposed method is good for learners of the game generation to get the help as scaffolding for learning math by educational games.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.67-79
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• 2018

In this paper, we present new generalized incomplete Pochhammer symbols and using this we introduce the extended generalized incomplete hypergeometric functions. We derive certain properties, generating functions and reduction formulas of these extended generalized incomplete hypergeometric functions. Special cases of this extended generalized incomplete hypergeometric functions are also discussed.

• Research in Mathematical Education
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• v.19 no.4
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• pp.267-278
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• 2015

The study is about the influence of literal, symbolic and graphics languages on mathematics reading. The results show that the scores of symbolic language volume are significantly lower than that of literal language volume. The abstractness of the mathematical symbols will not have a significant impact on the students with excellent mathematical academic, but as for the medium and poor students, abstract mathematics symbols will cause their cognitive impairment. Due to picture-superiority-effect, the test scores of the graphics language volume are significantly higher than that of the symbolic language volume. Graphics language will have a significant impact on the excellent and medium students, but has no impact on the poor students.

• Journal of the Korean Mathematical Society
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• v.31 no.2
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• pp.289-307
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• 1994

• Honam Mathematical Journal
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• v.43 no.1
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• pp.59-67
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• 2021

We characterize pluriharmonic symbols of the finite rank little Hankel operators on the Dirichlet space of the unit polydisk.