• 제목/요약/키워드: integral transform

검색결과 345건 처리시간 0.024초

APPLICATIONS OF THE REPRODUCING KERNEL THEORY TO INVERSE PROBLEMS

  • Saitoh, Saburou
    • 대한수학회논문집
    • /
    • 제16권3호
    • /
    • pp.371-383
    • /
    • 2001

  • In this survey article, we shall introduce the applications of the theory of reproducing kernels to inverse problems. At the same time, we shall present some operator versions of our fundamental general theory for linear transforms in the framework of Hilbert spaces.

  • PDF

A class of conditional analytic Feynman integrals

  • Chung, Dong-Myung;Kang, Si-Ho;Kang, Soon-Ja
    • 대한수학회논문집
    • /
    • 제11권1호
    • /
    • pp.175-190
    • /
    • 1996

  • In this paper we establish the existence of the conditional Feynman integral of certain functions which are not in the Banach algebra S of functions on Wiener space which are a kind of stochastic Fourier transform of complex Borel measures on $L^2[a, b]$. This result is used to provide the fundamental solution for the Schr$\ddot{o}$dinger equation for the forced harmonic potential.

  • PDF

A TIME-INDEPENDENT CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION PRODUCT ON AN ANALOGUE OF WIENER SPACE

  • Cho, Dong Hyun
    • 호남수학학술지
    • /
    • 제35권2호
    • /
    • pp.179-200
    • /
    • 2013

  • Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $X_n:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ by $Xn(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t$ is a partition of $[0,t]$. In the present paper, using a simple formula for the conditional expectation given the conditioning function $X_n$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions which have the form $$f((v_1,x),{\cdots},(v_r,x))\;for\;x{\in}C[0,t]$$, where {$v_1,{\cdots},v_r$} is an orthonormal subset of $L_2[0,t]$ and $f{\in}L_p(\mathbb{R}^r)$. We then investigate several relationships between the conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions.

  • https://doi.org/10.5831/HMJ.2013.35.2.179 인용 PDF KSCI