# Questions tagged [fa.functional-analysis]

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

5,629 questions
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### Exp-decay estimate of Schrodinger equation

Consider the equation $Hu=0$ with $u\in L^2(\Omega)$, where $H=-\Delta+V$ for some bounded continuous function $V$ and $\Omega$ is an un-bounded domain(e.g. $\mathbb R^n$). If $0$ is in discrete ...
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### Functional Analysis book with graphical descriptions [on hold]

I am looking for some book about functional analysis that has also graphical descriptions and images of the important concepts. Anyone knows some book like this?
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### Box counting dimension of a set and Lipschitz functions

If $f$ is Lipschitz, then the following holds for the Hausdorff dimension: $$\dim_H f(A) \le \dim_H A.$$ Is the same true for the box counting dimension?
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### Box counting dimension of the graph of the Cantor function

Consider the Cantor staircase function. The Hausdorff dimension of its graph is $1$. What is the box-counting dimension of its graph? A more general question is Box counting dimension of the graph of ...
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### An inequality for norms involving convolutions [migrated]

I need to prove/disprove the following existence theorem: $$\forall \epsilon > 0, \quad \exists f\in L^1(\mathbb R), g\in L^p(\mathbb R) : \quad (1-\epsilon)\|f\|_1\|g\|_p < \|f\ast g\|_p,$$ ...
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