# Questions tagged [fa.functional-analysis]

Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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### References for a class of Banach space-valued Gaussian processes

Let $E$ be a separable Banach space, consider a centered $E$-valued Gaussian process $\{x_t,t\ge 0\}$ that satisfies \mathbb{E}\phi(x_s)\psi(x_t)=R(s,t)K(\phi,\psi),\quad \phi,\psi\in ...
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### De la Vallée Poussin criterion on uniform integrability for infinite measures

The de la Vallée Poussin criterion (which is often used in combination with the Dunford-Pettis theorem) is usually formulated for probability measures/finite measures, for example in [Bogachev: ...
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### Dual of closure

Currently I'm studying about abstract interpolation theory for my research. One of the basic ways to construct new interpolation spaces, given an interpolation space $E$ with respect to a compatible ...
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### Compiling a List of Schauder Bases for Function Spaces

Schauder bases are fundamental tools in functional analysis, allowing us to represent functions within a space as infinite sums of basis elements. These bases play a crucial role in studying the ...
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### The size of super level sets and the symmetry on a sphere

Let $u$ be a smooth function defined on the sphere $\mathbb{S}^2$, and let $R \in \mathrm{SO}(3)$ be a three-dimensional rotation. Define $$S_R = \{x \in \mathbb{S}^2 : u(x) \neq u(Rx)\}.$$ Suppose ...
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