• Title, Summary, Keyword: Stieltjes functionals

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THE ANALYTIC FEYNMAN INTEGRAL OVER PATHS ON ABSTRACT WIENER SPACE

  • Yoo, Il
    • Communications of the Korean Mathematical Society
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    • v.10 no.1
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    • pp.93-107
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    • 1995
  • In their paper [2,3], Cameron and Storvick introduced some classes $S"+m$ and of functionals on classical Wiener spaces $C_0[a,b]$. For such functionals, they showed that the analytic Feynman integral exists and they gave some formulas for this integral. Moreover they obtained that the functionals of the form $$ (1.1) F(x) = exp {\int^b_a{\theta(s,x(x))dx} $$ are in S" where they assumbed that the potential $\delta : [a,b] \times R \to C$ satisfies (i) for each $s \in [a,b], \theta(s,\cdot)$ is the Fourier-Stieltjes transform of $\sigma_s \in M(R)$, (ii) for each Borel subset E of $[a,b] \times R, \sigma_s (E^{(s)})$ is a Borel measurable function of s on [a,b], and (iii) the total variation $\Vert \sigma_s \Vert$ of $\sigma_s$ is bounded as a function of s.tion of s.

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On A Symbolic Method for Error Estimation of a Mixed Interpolation

  • Thota, Srinivasarao
    • Kyungpook Mathematical Journal
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    • v.58 no.3
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    • pp.453-462
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    • 2018
  • In this paper, we present a symbolic formulation of the error obtained due to an approximation of a given function by the mixed-interpolating function. Using the proposed symbolic method, we compute the error evaluation operator as well as the error estimation at any arbitrary point. We also present an algorithm to compute an approximation of a function by the mixed interpolation technique in terms of projector operator. Certain examples are presented to illustrate the proposed algorithm. Maple implementation of the proposed algorithm is discussed with sample computations.

PARTS FORMULAS INVOLVING INTEGRAL TRANSFORMS ON FUNCTION SPACE

  • Kim, Bong-Jin;Kim, Byoung-Soo
    • Communications of the Korean Mathematical Society
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    • v.22 no.4
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    • pp.553-564
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    • 2007
  • In this paper we establish several integration by parts formulas involving integral transforms of functionals of the form $F(y)=f(<{\theta}_1,\;y>),\ldots,<{\theta}_n,\;y>)$ for s-a.e. $y{\in}C_0[0,\;T]$, where $<{\theta},\;y>$ denotes the Riemann-Stieltjes integral ${\int}_0^T{\theta}(t)\;dy(t)$.