• Title, Summary, Keyword: Orthonormal function

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ON THE ASYMPTOTIC CONVERGENCE OF ORTHONORMAL CARDINAL REFINABLE FUNCTIONS

  • Kim, Rae-Young
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.12 no.3
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    • pp.133-137
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    • 2008
  • We prove an extended version of asymptotic behavior of the orthonormal cardinal refinable functions from Blaschke products introduced by Contronei et al [2]. In fact, we show the orthonormal cardinal refinable function ${\varphi}_{k,q}$ converges in $L^p(\mathbb{R})$ ($2{\leq}p{\leq}{\infty}$) to the Shannon refinable function as ${\kappa}{\rightarrow}{\infty}$ uniforml on a class $\mathcal{Q}_{A,B}$ of real symmetric polynomials determined by positive constants $A{\leq}B$.

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CHARACTERIZATION OF ORTHONORMAL HIGH-ORDER BALANCED MULTIWAVELETS IN TERMS OF MOMENTS

  • Kwon, Soon-Geol
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.1
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    • pp.183-198
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    • 2009
  • In this paper, we derive a characterization of orthonormal balanced multiwavelets of order p in terms of the continuous moments of the multiscaling function $\phi$. As a result, the continuous moments satisfy the discrete polynomial preserving properties of order p (or degree p - 1) for orthonormal balanced multiwavelets. We derive polynomial reproduction formula of degree p - 1 in terms of continuous moments for orthonormal balanced multiwavelets of order p. Balancing of order p implies that the series of scaling functions with the discrete-time monomials as expansion coefficients is a polynomial of degree p - 1. We derive an algorithm for computing the polynomial of degree p - 1.

ORTHONORMAL BASIS FOR THE BERGMAN SPACE

  • Chung, Young-Bok;Na, Heui-Geong
    • Honam Mathematical Journal
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    • v.36 no.4
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    • pp.777-786
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    • 2014
  • We construct an orthonormal basis for the Bergman space associated to a simply connected domain. We use the or-thonormal basis for the Hardy space consisting of the Szegő kernel and the Riemann mapping function and rewrite their area integrals in terms of arc length integrals using the complex Green's identity. And we make a note about the matrix of a Toeplitz operator with respect to the orthonormal basis constructed in the paper.

Tomography Reconstruction of Ionospheric Electron Density with Empirical Orthonormal Functions Using Korea GNSS Network

  • Hong, Junseok;Kim, Yong Ha;Chung, Jong-Kyun;Ssessanga, Nicholas;Kwak, Young-Sil
    • Journal of Astronomy and Space Sciences
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    • v.34 no.1
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    • pp.7-17
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    • 2017
  • In South Korea, there are about 80 Global Positioning System (GPS) monitoring stations providing total electron content (TEC) every 10 min, which can be accessed through Korea Astronomy and Space Science Institute (KASI) for scientific use. We applied the computerized ionospheric tomography (CIT) algorithm to the TEC dataset from this GPS network for monitoring the regional ionosphere over South Korea. The algorithm utilizes multiplicative algebraic reconstruction technique (MART) with an initial condition of the latest International Reference Ionosphere-2016 model (IRI-2016). In order to reduce the number of unknown variables, the vertical profiles of electron density are expressed with a linear combination of empirical orthonormal functions (EOFs) that were derived from the IRI empirical profiles. Although the number of receiver sites is much smaller than that of Japan, the CIT algorithm yielded reasonable structure of the ionosphere over South Korea. We verified the CIT results with NmF2 from ionosondes in Icheon and Jeju and also with GPS TEC at the center of South Korea. In addition, the total time required for CIT calculation was only about 5 min, enabling the exploration of the vertical ionospheric structure in near real time.

ANALYTIC OPERATOR-VALUED GENERALIZED FEYNMAN INTEGRALS ON FUNCTION SPACE

  • Chang, Seung Jun;Lee, Il Yong
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.1
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    • pp.37-48
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    • 2010
  • In this paper we use a generalized Brownian motion process to defined an analytic operator-valued generalized Feynman integral. We then obtain explicit formulas for the analytic operatorvalued generalized Feynman integrals for functionals of the form $$F(x)=f\({\int}^T_0{\alpha}_1(t)dx(t),{\cdots},{\int}_0^T{\alpha}_n(t)dx(t)\)$$, where x is a continuous function on [0, T] and {${\alpha}_1,{\cdots},{\alpha}_n$} is an orthonormal set of functions from ($L^2_{a,b}[0,T]$, ${\parallel}{\cdot}{\parallel}_{a,b}$).

CARTIER OPERATORS ON COMPACT DISCRETE VALUATION RINGS AND APPLICATIONS

  • Jeong, Sangtae
    • Journal of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.101-129
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    • 2018
  • From an analytical perspective, we introduce a sequence of Cartier operators that act on the field of formal Laurent series in one variable with coefficients in a field of positive characteristic p. In this work, we discover the binomial inversion formula between Hasse derivatives and Cartier operators, implying that Cartier operators can play a prominent role in various objects of study in function field arithmetic, as a suitable substitute for higher derivatives. For an applicable object, the Wronskian criteria associated with Cartier operators are introduced. These results stem from a careful study of two types of Cartier operators on the power series ring ${\mathbf{F}}_q$[[T]] in one variable T over a finite field ${\mathbf{F}}_q$ of q elements. Accordingly, we show that two sequences of Cartier operators are an orthonormal basis of the space of continuous ${\mathbf{F}}_q$-linear functions on ${\mathbf{F}}_q$[[T]]. According to the digit principle, every continuous function on ${\mathbf{F}}_q$[[T]] is uniquely written in terms of a q-adic extension of Cartier operators, with a closed-form of expansion coefficients for each of the two cases. Moreover, the p-adic analogues of Cartier operators are discussed as orthonormal bases for the space of continuous functions on ${\mathbf{Z}}_p$.

ON 2-HYPONORMAL TOEPLITZ OPERATORS WITH FINITE RANK SELF-COMMUTATORS

  • Kim, An-Hyun
    • Communications of the Korean Mathematical Society
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    • v.31 no.3
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    • pp.585-590
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    • 2016
  • Suppose $T_{\varphi}$ is a 2-hyponormal Toeplitz operator whose self-commutator has rank $n{\geq}1$. If $H_{\bar{\varphi}}(ker[T^*_{\varphi},T_{\varphi}])$ contains a vector $e_n$ in a canonical orthonormal basis $\{e_k\}_{k{\in}Z_+}$ of $H^2({\mathbb{T}})$, then ${\varphi}$ should be an analytic function of the form ${\varphi}=qh$, where q is a finite Blaschke product of degree at most n and h is an outer function.

A Study on Design of Multivariable Equalizer for Transmission Distortion Compensation (전송왜곡보상용 다중가변등화기 설계에 관한 연구)

  • 김동석;최규훈;문홍진;김종교
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.27 no.6
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    • pp.921-928
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    • 1990
  • A multivariable equalizer is designed which compensates transmission distortion for coaxial transmission line. The characteristic transfer function with bilateral parameter domain is approximated using the expansion method of orthonormal function and Gram Schmidt orthogonal function, but the parameter domain of approximated function is limited to unilateral. To solve that problem, Bode type transfer function is used to give bilateral variable characteristic to approximated function. The multivariable equalizer in this paper can be substituted for the current equalizer which consist of a fixed equalizer and a variable equalizer.

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GENERALIZED FOURIER-WIENER FUNCTION SPACE TRANSFORMS

  • Chang, Seung-Jun;Chung, Hyun-Soo
    • Journal of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.327-345
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    • 2009
  • In this paper, we define generalized Fourier-Hermite functionals on a function space $C_{a,b}[0,\;T]$ to obtain a complete orthonormal set in $L_2(C_{a,b}[0,\;T])$ where $C_{a,b}[0,\;T]$ is a very general function space. We then proceed to give a necessary and sufficient condition that a functional F in $L_2(C_{a,b}[0,\;T])$ has a generalized Fourier-Wiener function space transform ${\cal{F}}_{\sqrt{2},i}(F)$ also belonging to $L_2(C_{a,b}[0,\;T])$.

Estimation of Excitation Forces from Measured Response Data (진동응답 계측결과를 이용한 기진력의 추정)

  • 한상보
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.1
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    • pp.45-60
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    • 1995
  • It is attempted to estimate excitation force of a linear vibratory system using measured vibration responses. The excitation force is estimated from the relationship between the vibration response and system characteristic matrices which are extracted from both the mathematical model of the system and actual response in contrast to the usual approach of inverting the frequency response matrices. This extraction scheme is based on the fact that the vibration response can be expressed in term of linear combination of frequency domain modal vectors defined as mutually orthonormal basis vectors in frequency domain. The extracted frequency domain basis vectors are very stable in computational manipulation. It is found that the estimated excitation force is in good agreement with actually measured force except at the natural frequencies the structure, which is the common feature still to be overcome by the research efforts in this area. From the results of this paper, this disagreement is considered to come from the discrepancy between the model and actual value of the mass, damping and stiffness of the structure.