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Results tagged with fourier-analysis
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user 15570
The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.
4
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0
answers
170
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Convergence of integral formula for Fourier inversion (and Hilbert transform) for integrable...
I asked the question below on Math Stack Exchange, https://math.stackexchange.com/questions/2592555/convergence-of-integral-formula-for-fourier-inversion-and-hilbert-transform-fo, but [despite it havi …
- 708
3
votes
2
answers
337
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How far can the domain of definition of multiplier operators be extended?
Given any $g \in L^\infty(\mathbb{R})$, we define the associated multiplier operator $T_g \colon L^2(\mathbb{R}) \to L^2(\mathbb{R})$ by
$$ \mathcal{F}(T_g f) \ = \ g.\mathcal{F}f $$
where $\mathcal{F …
- 708
0
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How far can the domain of definition of multiplier operators be extended?
I think I can now prove the following (which covers the case requested in the bounty):
Theorem. Let $g=P/Q$ for polynomials $P$ and $Q$ where $\mathrm{order}(P) \leq \mathrm{order}(Q)$ and $Q$ has no …
- 708