What are the functional characteristics of energy storage containers

Proving $f (x)=x$ from functional equation $f (2x-f (x))=x

$f$ satisfies the functional equation $fbigl (2x - f (x)bigr) = x$ for all $x in mathbb {R}$. Prove that $f (x)=x $ for all $x in mathbb {R}$. My thoughts: I have tried to use the given

2024 Sep 26

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What is the difference between an function and functional?

In the context of functional analysis, a functional is a function from a vector space to its base field (usually $mathbb {R}$ or $mathbb {C}$). In many important cases they are

2024 Dec 16

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Functional equation of real analytic Eisenstein series

A similar procedure is employed to obtain the analytic continuation and functional equation of the Epstein zeta function associated with positive definite binary quadratic forms,

2025 Dec 24

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Video lectures on Functional Analysis

I am looking for excellent VIDEO lectures on functional analysis. They should be (1) in English (2) the video quality and voice is good (3) the lecture should not be presented in

2025 Jul 31

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What is the difference between Real Analysis, Mathematical

What is the difference between Real Analysis, Mathematical Analysis, Functional Analysis, and Calculus? And is Analysis is the general field to all of them?

2025 Oct 23

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Give some example of linear functional?

A much more interesting example of a linear functional is this: take as your vector space any space of nice functions on the interval $ [0,1]$, for example the space of continuous

2024 Oct 23

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How to find the energy functional of a given PDE?

Existence does not even follow for ODE, there are some ODEs that do and can not have an associated Lagrangian (and therefore energy functional). This means they are not the

2025 Sep 10

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partial differential equations

In my PDE courses I''ve come across two different definitions or coercivity of a functional $mathit {F}: mathit {H} rightarrow mathbb {R}$ where $mathit {H}$ is a Hilbert

2025 Sep 27

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general topology

This leads to a variety of questions: The main being; What does the Minkowski Functional do? In the case of X not being a metric (non-metrizable) space,does the Minkowski

2025 Mar 14

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Good book for self study of functional analysis

It is a nice read for someone with only an undergrad analysis course. My favorite, although you might have trouble with your background, is Applications of Functional Analysis

2025 May 27

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