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Any irreducible tempered representation is a basic representation, and conversely any basic representation is the sum of a finite number of irreducible tempered representations. More precisely, it is a direct sum of 2 r irreducible tempered representations indexed by the characters of an elementary abelian group R of order 2 r (called the R ...
Examples include the class of all groups, the class of all vector spaces, and many others. In category theory, a category whose collection of objects forms a proper class (or whose collection of morphisms forms a proper class) is called a large category. The surreal numbers are a proper class of objects that have the properties of a field.
These identities also hold much more broadly in the sense of tempered distributions if one of f or g is a rapidly decreasing tempered distribution, a compactly supported tempered distribution or a Schwartz function and the other is a tempered distribution. On the other hand, two positive integrable and infinitely differentiable functions may ...
No matter what dual topology is placed on ′ (), [note 13] a sequence of distributions converges in this topology if and only if it converges pointwise (although this need not be true of a net). No matter which topology is chosen, D ′ ( U ) {\displaystyle {\mathcal {D}}^{\prime }(U)} will be a non- metrizable , locally convex topological ...
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
In mathematics, Schwartz space is the function space of all functions whose derivatives are rapidly decreasing.This space has the important property that the Fourier transform is an automorphism on this space.
In mathematics, economics and computer science, particularly in the fields of combinatorics, game theory and algorithms, the stable-roommate problem (SRP) is the problem of finding a stable matching for an even-sized set. A matching is a separation of the set into disjoint pairs ("roommates").
In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.