NOTATION In general, most of the notation in this work is the one commonly used in the subject, and part of it is borrowed from closely related works. However, we also employ some terminology which, unfortunately, has not been so standarized and its meaning in the literature tends to change from place to place. Thus, we find it convenient to summarize part of it here. We let 2= ^(lRn) and /= ^([Rn) be, respectively, the subspaces of C°°(IRn) of compactly supported functions and of Schwartz rapidly decreasing functions, with their usual topologies. Their duals are 2' and ^'(tempered distributions), while # ' (compactly supported distributions) is the dual of C°°(IRn). 9 is the space of all polynomials in Kn, and &Q = {ip e $f\ /^(x)p(x)dx = 0, V pG ^ } . The dual of &b with respect to the topology inherited from G/ is *f ' / &, the space of tempered distributions modulo polynomials. The usual tensor product of functions or distributions is denoted by ® . The Fourier transform of a tempered distribution f is denoted by f in case that f is, say, in , f (£) = / e ~ i x ^ f(x)dx. The inverse Fourier transform is denoted by By the bilinear form •, we denote the pairing between a test function and a distribution, or, more generally, between an element of a topological vector space X and one in its dual X . If T is a linear and continuous operator from a topological vector space X to another topological space Y, then, the formal transpose of T, denoted by T , is the continuous linear operator from Y to X , defined by vii
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