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In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin.
In mathematics, the logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm. The logarithmic norm was independently introduced by Germund Dahlquist [ 1 ] and Sergei Lozinskiĭ in 1958, for square matrices .
In mathematics, a locally integrable function (sometimes also called locally summable function) [1] is a function which is integrable (so its integral is finite) on every compact subset of its domain of definition. The importance of such functions lies in the fact that their function space is similar to L p spaces, but its members are not ...
is a function space.Its elements are the essentially bounded measurable functions. [2]More precisely, is defined based on an underlying measure space, (,,). Start with the set of all measurable functions from to which are essentially bounded, that is, bounded except on a set of measure zero.
In mathematics, a Hilbert–Schmidt integral operator is a type of integral transform.Specifically, given a domain Ω in n-dimensional Euclidean space R n, then the square-integrable function k : Ω × Ω → C belonging to L 2 (Ω×Ω) such that
In mathematics, the L p spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces.They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz ().
In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers.Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers.
For example, points (2, 0), (2, 1), and (2, 2) lie along the perimeter of a square and belong to the set of vectors whose sup norm is 2. In mathematical analysis, the uniform norm (or sup norm) assigns, to real-or complex-valued bounded functions defined on a set , the non-negative number
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