4 Sentences With "semi norms"

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Fréchet spaces can be defined in two equivalent ways: the first employs a translation-invariant metric, the second a countable family of semi- norms.
J. Duchon, 1976, Splines minimizing rotation invariant semi- norms in Sobolev spaces. pp 85–100, In: Constructive Theory of Functions of Several Variables, Oberwolfach 1976, W. Schempp and K. Zeller, eds., Lecture Notes in Math., Vol.
As the dimension increases there are some restrictions on the smallest order of differential that can be used, but actually Duchon's original paper,J. Duchon, 1976, Splines minimizing rotation invariant semi-norms in Sobolev spaces. pp 85–100, In: Constructive Theory of Functions of Several Variables, Oberwolfach 1976, W. Schempp and K. Zeller, eds., Lecture Notes in Math.
Every topological vector space , at least on a non discrete valued field gives a bornology on by defining a subset to be bounded (or von-Neumann bounded), if and only if for all open sets containing zero there exists a with . If is a locally convex topological vector space then is bounded if and only if all continuous semi-norms on are bounded on . If is a locally convex topological vector space, then an absorbing disk in is bornivorous (resp. infrabornivorous) if and only if its Minkowski functional is locally bounded (resp. infrabounded).