On the Fourier transform, Boehmians, and distributions
نویسندگان
چکیده
منابع مشابه
Distributions and Fourier Transform
Introduction. The theory of distributions, or generalized functions, provides a unified framework for performing standard calculus operations on nonsmooth functions, measures (such as the Dirac delta function), and even more general measure-like objects in the same way as they are done for smooth functions. In this theory, any distribution can be differentiated arbitrarily many times, a large c...
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1. Introduction. In this paper we consider the action of the Fourier transform on spaces of regular homogeneous distributions on R n , by which we mean to include the nonisotropic (sometimes called quasihomogeneous [6]) case. Specifically , consider the group of dilations of R n with positive scaling exponents dn x n) for δ > 0 (we will write this map as δ • x for short). Dilation induces scali...
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We have seen that the Fourier transform is well-behaved in the framework of Schwartz functions as well as L, while L is much more awkward. Tempered distributions, which include L, provide a larger framework in which the Fourier transform is well-behaved, and they provide the additional benefit that one can differentiate them arbitrarily many times! To see how this is built up, we start with a r...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2007
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm108-2-8