# Questions tagged [analysis]

Mathematical analysis. Consider a more specific tag instead: (real-analysis), (complex-analysis), (functional-analysis), (fourier-analysis), (measure-theory), (calculus-of-variations), etc. For data analysis, use (data-analysis).

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### Proof of $A\psi = \lambda \psi \Rightarrow h(A)\psi = h(\lambda)\psi$ on Borel functional calculus

Let $A: D(A) \to \mathscr{H}$ be a densely defined unbounded self-adjoint operator on a separable Hilbert space $\mathscr{H}$. By the Spectral Theorem, there exists some finite measure space $(M,\mu)$,...
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### Parity of Prolate Spheroidal Wave Functions.

I am trying to find a proof of the parity of the Prolate Spheroidal Wave functions $(\psi_{n})_{n}$, defined as the eigenfunctions of the differential operator $L_{c}\colon L^{2}[-1,1]\to L^{2}[-1,1]$,...
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### Why doesn't Cantor's diagonal argument also work for rational numbers? [duplicate]

Let's suppose that we don't know how to arrange all the rational numbers in such a way that easily shows that they're countably infinite. I present to you the following list which claims to include ...
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### LCH space and radon measure

I'm trying to solve this exercise, but I have some doubts: I think point (b) is correct, but I'm not sure about point (a). Let X be a locally compact Hausdorff topological space and let µ: S → [0, +∞] ...
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### Condition $\sum_{n=1}^\infty \left[ \sum_{m=1}^\infty a_{m,n}\right]$ and $\sum_{m=1}^\infty \left[ \sum_{n=1}^\infty a_{m,n}\right]$ to be equal

Consider real numbers $a_{m, n}$ for $n = 1 ,2,...$ and $m = 1, 2,...,$ an assume that inner and outer sums in the expressions \begin{align} A:= \sum_{n=1}^\infty \left[ \sum_{m=1}^\infty a_{m,n}\...
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