منابع مشابه
Pointwise Kernels of Schwartz Distributions
We show that Schwartz distributions have kernels in the class of the pointwise nonstandard functions. The main purpose of this note is to show that every Schwartz distribution T G 3' has a kernel /: *Rd —> *C in the class of the pointwise nonstandard functions in the sense that (1) (T,p)= [ f(xy<p(x)dx for all <p G 3, where *<p is the nonstandard extension of (p. Recall that, in general, the Sc...
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Employing two methods we consider a class of n-dimensional functional equations in the space of Schwartz distributions. As the first approach, employing regularizing functions we reduce the equations in distributions to classical ones of smooth functions and find the solutions. Secondly, using differentiation in distributions, converting the functional equations to differential equations and fi...
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Using a version of the sequential method we introduce a class of generalized functions called here "asymptotic functions''. This class contains kernels of all Schwartz distri butions and is equipped with a correctly defined multiplication operation. So, in a sense, one solves the problem of "multiplication of Schwartz distributions" although the solution refers to the class of the asymptotic f...
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It is argued that the criticisms by Schwartz and Schwartz of Jensen's analysis of IQ data on monozygotic twins reared apart fall down on two central points, methodological and theoretical: (a) Valid inferences concerning the broad heritability of intelligence can be drawn from analysis of the combined data from several independent studies of MZ twins reared apart, even though the groups differ ...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1977
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500002998