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In Simon's book Harmonic Analysis, example 3.5.12 shows: Fix $x \in \mathbb{R}^{\nu}$ (with $\left.\nu \geq 3\right), x \neq 0$ and define $f$ on $\{y:| y|<| x |\}$ by $$ f(y)=|x-y|^{-(\nu-2)}. $$ ...

My background : I am a Math PhD student. I will most probably work in harmonic analysis on Euclidean spaces. I am a fan of Folland's Real analysis and I have thoroughly studied first 8 chapters of ...

Let $f:(0,1) \to \mathbb R$ be a function that can be written as $$f(x) = \sum_{k=1}^\infty c_k \phi_k(x),$$ where $\phi_k(x) = \cos(\pi k x)$. What is the minimal assumption required on $f$ to ...