Journal of the Korean Mathematical Society (대한수학회지)
- Volume 33 Issue 3
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- Pages.541-555
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- 1996
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
HEAT EQUATION IN WHITE NOISE ANALYSIS
Abstract
The Fourier transform plays a central role in the theory of distribution on Euclidean spaces. Although Lebesgue measure does not exist in infinite dimensional spaces, the Fourier transform can be introduced in the space $(S)^*$ of generalized white noise functionals. This has been done in the series of paper by H.-H. Kuo [1, 2, 3], [4] and [5]. The Fourier transform $F$ has many properties similar to the finite dimensional case; e.g., the Fourier transform carries coordinate differentiation into multiplication and vice versa. It plays an essential role in the theory of differential equations in infinite dimensional spaces.