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The concept of an almost periodic function (also called a quasiperiodic function) was studied by Bohr, including work of Bohl and Escanglon. [47] He introduced the notion of a superspace. Bohr showed that quasiperiodic functions arise as restrictions of high-dimensional periodic functions to an irrational slice (an intersection with one or more ...
Quasiperiodic behavior is almost but not quite periodic. [2] The term used to denote oscillations that appear to follow a regular pattern but which do not have a fixed period. The term thus used does not have a precise definition and should not be confused with more strictly defined mathematical concepts such as an almost periodic function or a ...
For example, the Fourier series of a continuous T-periodic function need not converge pointwise. The uniform boundedness principle yields a simple non-constructive proof of this fact. In 1922, Andrey Kolmogorov published an article titled Une série de Fourier-Lebesgue divergente presque partout in which he gave an example of a Lebesgue ...
This is a list of some well-known periodic functions. The constant function f (x) = c, where c is independent of x, is periodic with any period, but lacks a fundamental period. A definition is given for some of the following functions, though each function may have many equivalent definitions.
A periodic function, also called a periodic waveform (or simply periodic wave), is a function that repeats its values at regular intervals or periods. The repeatable part of the function or waveform is called a cycle . [ 1 ]
An example of such a tiling is shown in the adjacent diagram (see the image description for more information). A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic . [ 3 ]
Bloch's theorem says that the eigenfunctions of a periodic Schrödinger equation (or other periodic linear equations) can be found in quasiperiodic form, and a related form of quasi-periodic solution for periodic linear differential equations is expressed by Floquet theory. Functions with an additive functional equation
One class that can be generated in this way is the rep-tiles; these tilings have unexpected self-replicating properties. [36] Pinwheel tilings are non-periodic, using a rep-tile construction; the tiles appear in infinitely many orientations. [37] It might be thought that a non-periodic pattern would be entirely without symmetry, but this is not so.