Dec 28, 2020 · I'm trying to organize my knowledge about Hardy spaces, especially $\mathcal{H}^1$.In Stein's book "Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals" there is quite comprehensive description of the properties of the real Hardy spaces in $\mathbb{R}^n$.

May 15, 2017 · In fact, check that $$\langle f,g \rangle = 2\pi \sum_{n}{a_n \overline{b_n}}$$ [Note that, even when you encounter a Banach space which you don't know the inner product formula for, you can thus check if it is a Hilbert space and describe an inner product.]

May 11, 2019 · The Hardy space $H^\infty(\mathbb{C_+})$ is defined to be the space of all functions $f$ >analytic and bounded on the complex right half plane $\mathbb{C_+}$ with the ...

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Oct 13, 2018 · To sum up, it is somehow enough to deal with energy signals that are described by the Hardy-Hilbert Space $\mathcal{H}_2$. As well as the Hardy space $\mathcal{H}_\infty$ is very useful to describe a broad range of uncertain linear systems.

Feb 6, 2017 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Nov 15, 2017 · $\mathcal{H}_2$ and $\mathcal{H}_\infty$ are Hardy Spaces for functions with bounded 2- / respectively infinity-norm, and (as described in the paper) $\mathcal{RH}_2$ and $\mathcal{RH}_\infty$ are the set of real-rational strictly proper / proper transfer matrices. This still makes sense to me.

Oct 19, 2017 · There are things called "complex Riesz spaces", which are defined as the complexification of a Riesz space. But the Hardy space of holomorphic functions is not the complexification of a real function space; indeed it doesn't …

Apr 20, 2021 · What text would you recommend for a (not too long) introduction to Hardy spaces? I am specially interested in real Hardy spaces but I also want to learn about complex ones. I'm a graduate student with some background in harmonic, complex and functional analysis.

Dec 31, 2017 · Product of functions in Hardy space. 1. Alternative definition of Hardy spaces. 1.