• The Mathematical Education
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• v.22 no.1
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• pp.73-75
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• 1983

• The Mathematical Education
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• v.19 no.1
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• pp.51-53
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• 1980

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.613-635
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• 1998

In this note we reformulate the white noise calculus on the classical Wiener space (C', C). It is shown that most of the examples and operators can be redefined on C without difficulties except the Hida derivative. To overcome the difficulty, we find that it is sufficient to replace C by L$_2$[0,1] and reformulate the white noise on the modified abstract Wiener space (C', L$_2$[0, 1]). The generalized white noise functionals are then defined and studied through their linear functional forms. For applications, we reprove the Ito formula and give the existence theorem of one-side stochastic integrals with anticipating integrands.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.977-994
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• 2004

A pair of quasi-definite linear functionals {u$_{0}$, u$_1$} is a generalized $\Delta$-coherent pair if monic orthogonal polynomials (equation omitted) relative to u$_{0}$ and u$_1$, respectively, satisfy a relation (equation omitted) where $\sigma$$_{n}$ and T$_{n}$ are arbitrary constants and $\Delta$p = p($\chi$＋1) - p($\chi$) is the difference operator. We show that if {u$_{0}$, u$_1$} is a generalized $\Delta$-coherent pair, then u$_{0}$ and u$_{1}$ must be discrete-semiclassical linear functionals. We also find conditions under which either u$_{0}$ or u$_1$ is discrete-classical.ete-classical.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.73-82
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• 2016

The utility of exponential generating functions is that they are relevant for combinatorial problems involving sets and subsets. Sequences of polynomials play a fundamental role in applied mathematics, such sequences can be described using the exponential generating functions. The actuarial polynomials ${\alpha}^{({\beta})}_n(x)$, n = 0, 1, 2, ${\cdots}$, which was suggested by Toscano, have the following exponential generating function: $${\limits\sum^{\infty}_{n=0}}{\frac{{\alpha}^{({\beta})}_n(x)}{n!}}t^n={\exp}({\beta}t+x(1-e^t))$$. A linear functional on polynomial space can be identified with a formal power series. The set of formal power series is usually given the structure of an algebra under formal addition and multiplication. This algebra structure, the additive part of which agree with the vector space structure on the space of linear functionals, which is transferred from the space of the linear functionals. The algebra so obtained is called the umbral algebra, and the umbral calculus is the study of this algebra. In this paper, we investigate some umbral representations in the actuarial polynomials.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.59-66
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• 2001

A class of topological algebras, which we call it a fundamental one, has already been introduced to generalize the locally bounded and locally convex algebras. To prove the basic theorems on fundamental algebras, the first successful step is the new version of the Cohen factorization theorem. Here we recall it and prove some new results on fundamental topological algebras.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.95-100
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• 1998

In this note we consider some basic facts concerning abstract M spaces and investigate extremal structure of the unit ball of bounded linear functionals on $\sigma$-complete abstract M spaces.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.537-542
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• 2000

When A is a subalgebra of a $C^*$-algebra, the spatial numerical range of element of A can be described in terms of positive linear functionals on the $C^*$-algebra.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.377-387
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• 2006

In this paper, some characterizations of representation for continuous linear functionals on $2{\kappa}$-inner product spaces in terms of best approximations and orthogonalities are given.

• The Pure and Applied Mathematics
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• v.6 no.1
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• pp.47-52
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• 1999

In this note we give a characterization on weak convergence of bounded linear functionals in $\sigma$-complete abstract M spaces.