• 호남수학학술지
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• 제22권1호
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• pp.31-36
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• 2000

In this paper, we introduce the extremal length and examine its properties and consider the applications of extremal length to conformal mappings. We obtain the theorems in the connection with "the extremal length zero" and "the fundamental sequences".

• 대한수학회논문집
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• 제21권1호
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• pp.135-143
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• 2006

We consider some applications of extremal length to the boundary behavior of analytic functions and derive theorems in connection with the conformal mappings. It shows us the usefulness of the method of extremal length. And we present some geometric applications of extremal length. The method of extremal length lead to simple proofs of theorems.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.603-611
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• 2005

We present some geometric applications of extremal length. The method of extremal length leads a simple proofs of theorems. And we consider the applications of extremal length to the boundary behavior of analytic functions and derive theorems in connection with the conformal mappings. It shows us the usefulness of the method of extremal length.

• 충청수학회지
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• 제12권1호
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• pp.193-196
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• 1999

In this note, we present some geometric applications of extremal length to analytic functions. We drive an interesting formula by the method of extremal length.

• 충청수학회지
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• 제16권1호
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• pp.49-60
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• 2003

In this note, we introduce the concept of the extremal length of a curve family in the complex plane and apply the extremal length to the boundary behavior of analytic functions. We consider some geometric applications of extremal length and establish applications connected with the logarithmic capacity.

• 충청수학회지
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• 제20권2호
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• pp.147-156
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• 2007

We introduce the extremal length and examine its properties. And we consider the geometric applications of extremal length to the boundary behavior of analytic functions, conformal mappings. We derive the theorem in connection with the capacity. This theorem applies the extremal length to the analytic function defined on the domain with a number of holes. And we obtain the theorems in connection with the pure geometric problems.

• 대한수학회지
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• 제44권6호
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• pp.1291-1312
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• 2007

We study some extremal problems on the Cartan-Hartogs domains. Through computing the minimal circumscribed Hermitian ellipsoid of the Cartan-Hartogs domains, we get the $Carath\acute{e}odory$ extremal mappings between the Cartan-Hartogs domains and the unit hyperball, and the explicit formulas for computing the $Carath\acute{e}odory$ extremal value.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.495-502
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• 2004

We consider the applications of extremal length to the boundary behavior of analytic functions and derive a theorem in connection with the capacity. This theorem applies the extremal length to the analytic functions defined on the domain with a number of holes. So it shows us the usefulness of the method of extremal length.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.547-551
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• 1998

We give some examples of extremal minimal free reso-lutions of Gorenstein ideals of codimension 4.

• 대한수학회논문집
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• 제32권4호
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• pp.875-883
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• 2017

In this work, we establish Heisenberg-type uncertainty principle for the Bessel-Struve Fock space ${\mathbb{F}}_{\nu}$ associated to the Airy operator $L_{\nu}$. Next, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator $T:{\mathbb{F}}_{\nu}{\rightarrow}H$, where H be a Hilbert space. Furthermore, we come up with some results regarding the extremal functions, when T are difference operators.