The Russian version of this publication seemed five years in the past. considering the fact that that point, many effects were more desirable upon and new techniques to the issues investigated within the booklet have seemed. however the maximum shock for us was once to find that there exists a wide team of mathematicians operating within the sector of the so-called White Noise research that's heavily hooked up with the fundamental a part of our booklet, particularly, with the speculation of generalized capabilities of infinitely many variables. the 1st papers facing White Noise research have been written through T. Hida in Japan in 1975. Later, this research used to be devel oped intensively in Japan, Germany, u.s., Taipei, and in different places. The comparable difficulties of infinite-dimensional research were studied in Kiev considering that 1967, and the idea of generalized features of infinitely many variables has been in vestigated on account that 1973. even if, as a result of political procedure within the U.S.S.R., touch be tween Ukrainian and international mathematicians was once very unlikely for a protracted time period. the reason is,, to our nice remorse, simply on the finish of 1988 did one of many authors meet L. Streit who advised him in regards to the life of White Noise research. And it develop into transparent that many ends up in those theories coincide and that, in reality, there exists a unmarried conception and never detailed ones.
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