Functional analysis is the study of infinite-dimensional vector spaces, often with additional structures (inner product, norm, topology), with typical examples given by function spaces. The subject also includes the study of linear and non-linear operators on these spaces, as well as measure, ...

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Biharmonic Equation in a Rectangle with Some Uncommon Boundary Conditions

Consider the following boundary value problem (BVP) $$\matrix{ {{\Delta ^2}H = 0,} \hfill & {} \hfill & {{\rm{in}}\,} \hfill & \Omega \hfill \cr {\partial _y^2H = 0} \hfill & ...
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Proving that if $f\in\mathcal{F}C^{1}_{b}(X)$ then $f\in W^{1,p}(X,\gamma$) for $p>1$

Let $X$ be a separable Banach space endowed with a centered nondegenerate Gaussian measure $\gamma$ and $H$ the Cameron-Martin space. Then consider $f\in\mathcal{F}C^{1}_{b}(X)$. I want to prove that ...
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how to show this function has zeros interlacing and including those of Riemann zeta

Let $\chi (t) = H \left( - \frac{i}{2} (2 t - 1) \right) = \dfrac{4 i \pi \zeta (t) \left( \left( \ddot{\Psi} \left(\frac{t}{2} \right) - \ddot{\Psi} \left( \frac{1}{2} - \frac{t}{2} \right)\right) ...