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15h
revised Is this operator a Fourier multiplier operator?
added 77 characters in body
15h
comment Is this operator a Fourier multiplier operator?
@CameronWilliams Consider $f(t)*\frac{e^{i\alpha t}}{t}$, I want to take a derivative of this and then look at it as a fourier multiplier acting on f, but looks like such a thing is possible only through tempered distribution. Please look at this answer and suggest me something how to move forward.
15h
comment Is this operator a Fourier multiplier operator?
@JoãoRamos Consider $f(t)*\frac{e^{i \alpha t}}{t}$, I want to take a derivative of this and then look at it as a fourier multiplier acting on $f$, but looks like such a thing is possible only through tempered distribution. Please look at this answer and suggest me something how to move forward.
17h
comment Is this operator a Fourier multiplier operator?
@JoãoRamos : I understand the integral won't converge, I want to understand how I can use this distribution conceptually, in my problem. It appears that the rules are different here with distributions than functions (as per my experience) but I dont know the rules.
18h
comment Is this operator a Fourier multiplier operator?
@CameronWilliams : It would be great if you can explain it in an answer, and how to make sense of a distribution.
18h
comment Is this operator a Fourier multiplier operator?
@CameronWilliams : I dont want to compute Fourier transform of $f$, $f$ is a generic function in my analysis. So What you said is true, I want Fourier transform of $L_{\alpha}$ and then I multiply it with FT of $f$. I don't know much about distributions, so I don't get what is not clearer, it appears to me that you have answered my question, but I don't know how to deal with distributions, perhaps that where I am missing the point.
18h
comment Is this operator a Fourier multiplier operator?
@JoãoRamos : Yes, please feel free to use distributions. Ultimately I am tryinng to solve this problem, and I hope distributions can take me there. mathoverflow.net/a/210787/14414
18h
asked Is this operator a Fourier multiplier operator?
Jul
4
accepted Change of order of integration of a triple integral
Jul
4
comment Change of order of integration of a triple integral
Seems reasonable, +1;
Jul
4
awarded  Popular Question
Jul
4
comment Change of order of integration of a triple integral
Dude I am out of touch with these things, I had done this a few days back, that time I followed a video in youtube, but could not convince myself it was really correct, thats why I am asking this question. Please help me if you can.
Jul
4
comment Change of order of integration of a triple integral
Could you please write down the expression (answer) for me?
Jul
4
asked Change of order of integration of a triple integral
Jun
25
comment what does `ensemble average` mean?
@Ian : Oh, I dealt with physics only till High school. For engineers, phase has a totally different purpose, like the phase angle of a sinusoidal signal, etc... No wonder the word "phase" not being used by engineers in context of stochastic processes. Good to know it has totally different meaning in physics.
Jun
25
comment what does `ensemble average` mean?
@Ian : Sorry, i am an engineer by training in electronics and communication systems, we study stochastic processes, and have never heard of the term 'phase space'.
Jun
25
comment what does `ensemble average` mean?
@Ian : quoting OP : "not only in this context but the exact meaning and use of ensemble averaging in statistics and mathematics."
Jun
25
answered what does `ensemble average` mean?
Jun
25
comment Is the Cauchy-Schwarz inequality ever used in Physics?
I fail to understand what is your motivation for such a question.
Jun
25
comment Is the Cauchy-Schwarz inequality ever used in Physics?
only drawback is that, one of the vector is always an unit vector, so it doesnt use the Cauchy-Schwartz inequality in full generality, neverthless it is more physical example than the one given by Ittay.