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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

1 vote
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Function in $B(\mathbb{R})$

You may be aware of this already, but a similar (if not the same) question is addressed in Rudin's Fourier Analysis on Groups. Material on the same subject can be found in Katznelson's Harmonic analys …
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1 vote

Spectra on different spaces

I know it's a while since this question was asked, but I think the book "Linear Operators and their Spectra" by E. Brian Davies might contain some information about what's being asked here. In particu …
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  • 778
1 vote

Rigorous justification for this formal solution to $f(x+1)+f(x)=g(x)$

Just to add another answer to the pile... I suspect that the 'magic' observed here may be related to so-called local spectral theory. It is possible to do quite a lot (at least in the Banach space se …
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