• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.227-233
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• 2002

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation AX$\sub$i/=Y$\sub$i/, for i=1,2, ‥‥, R. In this article, we investigate Hilbert-Schmidt interpolation for operators in tridiagonal algebras.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.725-732
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• 2021

This paper aims to present a new lower bound for some inequalities related to Frames in Hilbert space. Some refinements of the inequalities for general frames and alternate dual frames under suitable conditions are given. These results refine the remarkable results obtained by Balan et al. and Gavruta.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.59-72
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• 2024

In the presented paper, the first section contains strong convergence and demiclosedness property of a sequence generated by Karakaya et al. iteration scheme in a Hilbert space for quasi-nonexpansive mappings and also the comparison between the iteration scheme given by Karakaya et al. with well-known iteration schemes for the convergence rate. The second section contains some applications of the fixed point theory in solution of different mathematical problems.

• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.237-243
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• 2024

A similarity transformation of a solution of the Cauchy problem for the linear difference equation in Hilbert space has been studied. In this manuscript, we obtain necessary and sufficient conditions for linear equivalence of the discrete semigroup of operators, generated by the solution of the difference equation utilizing four Canonical semigroups.

• 대한수학회지
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• 제32권3호
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• pp.447-459
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• 1995

A fundamental problem is to construct linear systems with given transfer functions. This problem has a well known solution for unitary linear systems whose state spaces and coefficient spaces are Hilbert spaces. The solution is due independently to B. Sz.-Nagy and C. Foias [15] and to L. de Branges and J. Ball and N. Cohen [4]. Such a linear system is essentially uniquely determined by its transfer function. The de Branges-Rovnyak construction makes use of the theory of square summable power series with coefficients in a Hilbert space. The construction also applies when the coefficient space is a Krein space [7].

• 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.

• 호남수학학술지
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• 제27권4호
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• pp.621-629
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• 2005

We consider the stability of Hilbert space framelets and related Riesz frames. Our results are in spirit close to classical results for orthonormal bases, due to Mazur and Schauder.

• 대한수학회논문집
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• 제10권2호
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• pp.401-407
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• 1995

The best constants for two distinct weak-type inequalities for martingales and their differential subordinates with values in some spaces isomorphic to a Hilbert space are shown to be the same. This extends the result of Burkholder shown in the Hilbert space setting.

• Journal of the Korean Data and Information Science Society
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• 제16권2호
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• pp.411-418
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• 2005

We review support vector and wavelet density estimation. The relationship between support vector and wavelet density estimation in reproducing kernel Hilbert space (RKHS) is investigated in order to use wavelets as a variety of support vector kernels in support vector density estimation.

• 대한수학회보
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• 제23권2호
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• pp.141-148
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• 1986

In [1], M. Guignard considered a constraint set in a Banach space, which is similar to that in [2] and gave a first order necessary optimality condition which generalized the Kuhn-Tucker conditions [3]. Sufficiency is proved for objective functions which is either pseudoconcave [5] or quasi-concave [6] where the constraint sets are taken pseudoconvex. In this note, we consider a psedoconvex programming problem in a Hilbert space. Constraint set in a Hillbert space being pseudoconvex and the objective function is restrained by an operator equation. Then we use the methods similar to that in [1] and [6] to obtain a necessary and sufficient optimality condition.