Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hamzabellouch/agent-skills --skill functional-analysis-and-fouriergit clone --depth 1 https://github.com/hamzabellouch/agent-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hamzabellouch/agent-skills/functional-analysis-and-fourier)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/functional-analysis-and-fourier"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/functional-analysis-and-fourier/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/functional-analysis-and-fourier"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/functional-analysis-and-fourier.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00061 | $0.00593 |
| Opus 5.5 | $0.00024 | $0.00237 |
| Sonnet 5.5 | $0.00012 | $0.00119 |
| Haiku 4.5 | $0.00006 | $0.00059 |
Grade A, and why
functional-analysis-and-fourier scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured today.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 28 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Functional Analysis & Fourier Analysis
Normed spaces
- Banach spaces (complete normed), Hilbert spaces (complete inner product). l^p, L^p, C(K) with sup norm.
- Bounded linear operators B(X,Y): norm ||T||; continuity <=> boundedness. Dual space X*, Riesz representation (Hilbert space H* = H).
- Big theorems: Hahn-Banach (extension of functionals), Uniform boundedness (Banach-Steinhaus), Open mapping, Closed graph, Banach-Alaoglu (weak-* compactness).
- Weak topologies, reflexivity, compact operators (Fredholm alternative), Fredholm index.
- Spectrum sigma(T): resolvent set; spectral theorem for compact self-adjoint operators (diagonalizable with real eigenvalues), for bounded/unbounded self-adjoint operators (projection-valued measure). Application: quantum observables.
- Banach algebras, C*-algebras, Gelfand transform; semigroups of operators (e^{tA}) for PDE evolution (Hille-Yosida).
Distributions and Sobolev spaces
Test functions, distributions (delta, principal value), weak derivatives; Sobolev W^{k,p} and H^s; Sobolev embedding; trace theorem; Poincare inequality; Lax-Milgram for elliptic PDE.
Fourier analysis
- Fourier series: coefficients c_n = (1/2 pi) integral f e^{-int}; Parseval sum |c_n|^2 = (1/2 pi) integral |f|^2; Gibbs phenomenon; convergence (Dirichlet, Fejer averages).
- Fourier transform f^(xi) = integral f(x) e^{-i x xi} dx; Plancherel; convolution <-> product; derivative <-> multiplication by i xi; Gaussians map to Gaussians; uncertainty principle sigma_x sigma_xi >= 1/2; Poisson summation; sampling theorem (Shannon-Nyquist).
- Discrete: DFT and FFT O(n log n); windowing; spectral leakage.
- Wavelets: multiresolution analysis, Haar and Daubechies; time-frequency analysis, Gabor transform; applications in compression and denoising.
- Harmonic analysis on groups: characters, Pontryagin duality, Peter-Weyl.
Tip
In infinite dimensions, finite-dimensional intuition can fail: closed bounded sets need not be compact, operators may have continuous spectrum, and domains of unbounded operators matter.
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- today First seen · 28 lines · 61 tokens per session scan A 1718c0b2760c
functional-analysis-and-fourier is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 61 tokens to every session and 593 once invoked, about $0.0002 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-17.
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