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As a matter of fact, the poster is right on the other side of the hall in front of my office. Here is a picture of Dehn that I've made with my phone: I could make a better picture on Monday if that w …

The version 2 is also popular among electrical engineers as the variable $\xi$ is then the actual frequency. For an electrical engineering view on the Fourier transform, I can recommend the lecture no …

Also a borderline suggestion since it is rather multilinear than just linear: Recent progress on low rank tensor approximation for all kinds of different applications within mathematics. A list of app …

In "THE SEQUENCE SPACES $l(p_\nu)$ AND $m(p_\nu)$" by S. Simons there is the following theorem about sequence spaces of $l_p$-type with varying exponents which is attributed (without a more precise re …

I don't know who deserves credit for this, but I was stunned by the concept of view complicated objects like functions simply as points in a vector space. With that view one solves and analyzes PDEs o …

Arrow's impossibility theorem comes to mind. To quote Wikipedia: In short, the theorem states that no rank-order electoral system can be designed that always satisfies these three "fairness" criteria …

The book "Der Briefwechsel Richard Dedekind – Heinrich Weber" transcribes the full correspondence between the two. From the description: This volume provides the very first transcription of correspon …

David Mumford, a well known algebraic geometer, is responsible for the "Mumford-Shah segmentation" model in mathematical imaging. Besides being one of the most cited papers in this area, it also spark …

Well, this is basically the same answer as the one by Alexandre Eremenko, but here goes: The particular form of the definition of derivative is crucial for partial differential equations. Using weaker …

The book "De wilde getallen" by Philibert Schogt ("The wild numbers") is a great story about a young mathematician and his struggle with an (imaginary) theorem in number theory. It illustrates the emo …

I think Carlo Beenakker digged up the right reference for the notation of the set, but I think more can be said. First, there is some meaning for the subscript $0$ which can be found in the same pape …

The Wikipedia page for the Shannon-Whittaker reconstruction formula states that Whittaker used the term "cardinal series" for the reconstruction formula $$ f(t) = \sum_{n\in\mathbb{N}} f(n)\mathrm{sin …

$H=W$

I think that these spaces don't go under the name of $L$ spaces anymore. Actually, I am not sure if there is a consensus on how these structures are called today. A good place to start is the fairly r …

Another, not too mathematical, analogy comes from image processing. There you can consider an image $u$ as a real valued function on a rectangle, say. A basic method for edge detection is to calculate …