# Tagged Questions

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### The influence of eigendecomposition on the periodicity of a (rank 2) Hermitian matrix (of functions)

Let $\boldsymbol{R}(u,v);~u,v\in\mathbb{R}$ be a Hermitian matrix (of Hermitian functions) with entries r_{ij}(u,v) = 1 + Ae^{-2\pi i \phi_{ij}(ul_0 + vm_0)}; ...
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### computing a certain contour integral [closed]

I want to compute an integral along a vertical line segment. The function I'm integrating involves the zeta-function, and usually the way such integrals are done treats the line segment as one side ...
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### An integral with Gamma functions (Part 2)

I was wondering if there is a generalization of the integral discussed here to a case like, \int \frac{d^dq}{q^{\nu_1}\vert \vec{q} \pm \vec{k}_1\vert ^{\nu_2}\vert \vec{q} \pm ...
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### The Paley-Wiener theorem and exponential decay.

Consider a function whose Fourier transform is supported on a half-ray: $$A(t)=\int_0^\infty \omega(E) e^{-iEt}d E,$$ where I can suppose $\omega(E)\geq 0$ and any suitable regularity conditions on ...
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### Characteristic Function of a Non-negative Random Variable Evaluated at a Complex Value

Suppose we have a non-negative random variable $X$ with density $p(x)$,and its characteristic function, evaluated at a complex number $z$, being $\phi(z)=E[e^{z X}]=\int_{0}^{\infty}e^{zx}p(x)dx$. It ...
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### In Fourier Transforms: Positive Definite Functions, Bochner's Theorem, and Derivatives

I've been reading about Bochner's Theorem lately, but when I apply it to the derivative of a function, I seem to get a contradiction with the theorem. "Bochner's theorem states that a positive ...