Rajesh D
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 Nov 24 comment Linear continuous functional that is not uniformly continuous. @Jochen : The vector metric space, described in this paper page 425. and rest of paper. ams.org/journals/tran/1936-040-03/S0002-9947-1936-1501882-8/… Nov 19 revised Linear continuous functional that is not uniformly continuous. deleted 1 character in body; edited title Nov 18 asked Linear continuous functional that is not uniformly continuous. Nov 1 awarded Yearling Sep 11 awarded Notable Question Sep 4 comment Is there any pde whose solution evolves as a partial Fourier integral? Good to see you back on math.SE. I need some advice regarding a problem in Fourier analysis. Could you please pass me your latest email id. Thanks Sep 4 accepted Is there any pde whose solution evolves as a partial Fourier integral? Sep 3 comment Is there any pde whose solution evolves as a partial Fourier integral? @WillieWong : In your formula, I guess the integration is with respect to $s$ instead of $x$. Could you please add this as an answer, so I can accept it. Sep 2 awarded Popular Question Jul 16 asked Is there a specific and useful strategy for this kind of general setup of a problem? Jul 15 accepted How does this conjecture correspond to Carleson's theorem for the case of $d=1$? Jul 14 asked How does this conjecture correspond to Carleson's theorem for the case of $d=1$? Jul 13 comment Is this operator a Fourier multiplier operator? In my case, $f$ is a generic function, it may contain jump discontinuties. Basically it is a function of bounded variation. So how can I handle this definition in my problem? Jul 10 comment Is this operator a Fourier multiplier operator? great! looking forward Jul 10 comment Is this operator a Fourier multiplier operator? If you don't find it interesting, then no problem. Jul 10 comment Is this operator a Fourier multiplier operator? You know my motivational problem, so why not substitute this expression there and take it forward to see what can be done in proving it, I offer you a joint publication! Jul 10 comment Is this operator a Fourier multiplier operator? ok, no problem. I should really thank you for the nice answer. Jul 10 comment Is this operator a Fourier multiplier operator? Ah, then I feel $x$ should replace $y$ in the expression sitting inside the Hilbert operator, that would avoid confusion and there really isnt any need for $y$ when we can do with $x$. I mean we cannot write for example $f(x) \ast g(y) \ast h(t)$ right we just have to write $f(t)\ast y(t) \ast h(t)$ . Correct me if I got it wrong. I agree you needed $y$ inside the integral to explain principal value, but later it can be avoided. Jul 10 comment Is this operator a Fourier multiplier operator? I don't get what two variables $x$,$y$ doing in this single expression $$\pi e^{i\alpha x} \mathcal{H}(e^{-iy\alpha}f)$$, and $t$ not appearing, may be I assume $x$ was taken instead of $t$ but what is $y$ doing in it. This I think I probably not getting the context here, as I am not having working knowledge on distributions. It would help if you could throw some light on it. Jul 10 revised Is this operator a Fourier multiplier operator? added 273 characters in body