• Honam Mathematical Journal
• /
• v.35 no.3
• /
• pp.389-394
• /
• 2013

It is an interesting problem to study fixed points of an element in the holonomy group of an affine manifold. We compute the limit of a sequence of projective transformations and verify relations between fixed points and kernels.

• Honam Mathematical Journal
• /
• v.20 no.1
• /
• pp.79-88
• /
• 1998

In this paper we define the concept of $Fr{\acute{e}}chet$ function algebras on hemicompact spaces. So we show that under certain condition they can be represented as a projective limit of Banach function algebras. Then the class of $Fr{\acute{e}}chet$ Lipschitz algebras on hemicompact metric spaces are defined and their relations with the class of lipschitz algebras on compact metric spaces are studied.

• Kyungpook Mathematical Journal
• /
• v.29 no.2
• /
• pp.203-236
• /
• 1989

• East Asian mathematical journal
• /
• v.24 no.1
• /
• pp.97-103
• /
• 2008

New fixed point theorems for permissible maps between $Fr{\acute{e}}chet$ spaces are presented. The proof relies on index theory developed by Dzedzej and on viewing a $Fr{\acute{e}}chet$ space as the projective limit of a sequence of Banach spaces.

• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.69-83
• /
• 2009

New Lefschetz fixed point theorems for compact absorbing contractive admissible maps between Frechet spaces are presented. Also we present new results for condensing maps with a compact attractor. The proof relies on fixed point theory in Banach spaces and viewing a Frechet space as the projective limit of a sequence of Banach spaces.

• Journal of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.547-564
• /
• 2024

We study totally real and complex subsets of a right quarternionic vector space of dimension n + 1 with a Hermitian form of signature (n, 1) and extend these notions to right quaternionic projective space. Then we give a necessary and sufficient condition for a subset of a right quaternionic projective space to be totally real or complex in terms of the quaternionic Hermitian triple product. As an application, we show that the limit set of a non-elementary quaternionic Kleinian group 𝚪 is totally real (resp. commutative) with respect to the quaternionic Hermitian triple product if and only if 𝚪 leaves a real (resp. complex) hyperbolic subspace invariant.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.4
• /
• pp.785-803
• /
• 2004

We research properties of analytic functions which are exponentially decreasing or increasing. Also we show that the space of test functions is dense in the space of extended Fourier hyper-functions, and that the Fourier transform of the space of extended Fourier hyperfunctions into itself is an isomorphism and Parseval's inequality holds.

• Communications of the Korean Mathematical Society
• /
• v.19 no.4
• /
• pp.661-681
• /
• 2004

We research properties of the space of measurable functions square integrable with weight exp$2\nu $\mid$x$\mid$$, and those of the space of Fourier hyperfunctions. Also we show that the several embedding theorems hold true, and that the Fourier-Lapace operator is an isomorphism of the space of strongly decreasing Fourier hyperfunctions onto the space of analytic functions extended to any strip in $C^n$ which are estimated with the aid of a special exponential function exp($\mu$｜x｜).

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.259-267
• /
• 2002

Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.

• Journal of the Architectural Institute of Korea Planning & Design
• /
• v.34 no.11
• /
• pp.125-134
• /
• 2018

This study examines Dalibor Vesely's theoretical proposition of communicative space and tries to develop it through a review of the contemporary architectural case. Vesely poses a critical question about communication: how do the situational conditions of our everyday life and the spatial characteristics of the natural world in which we live communicate through representation. He emphasizes the spatial and situational conditions and the role of representation in communication, arguing that architecture should create the formation of communicative space to restore its primary role as the corporeal foundation of culture. This study thus focuses on one of the critical concepts of his theory: "the communicative movement," which is, according to him, ontological and situational because it animates and transforms human circumstances as a whole. Further, it pursues some practical knowledge of creating the communicative space, by examining the design theory and practice of Zaha Hadid, who thematizes communication and movement in her architectural approach. This study analyses the different levels of representation and modes of movement in her architectural space to reveal the possibilities and limits of its communicative roles. We will find that the representation of Hadid's architectural space is not the formal representation of reality, but a mathematical and projective representation of abstract concepts. Despite its apparent aesthetic consistency, the inward and self-referential relation between the individual elements of the architectural space reveals its limit for the communicative space.