Fréchet space

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Fréchet space

[frā′shā ‚spās]
(mathematics)
A topological vector space that is locally convex, metrizable, and complete.
A topological vector space that is metrizable and complete.
T1 space
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References in periodicals archive ?
Since [S.sub.[omega]](R) is a Frechet space, we have from Banach-Steinhaus theorem that T is linear and continuous; that is, T [member of] [S'.sub.[omega]](R).
Periodic Tempered Distributions of Beurling Type and Periodic Ultradifferentiable Functions with Arbitrary Support
Given Frechet space R([F.sub.1],...,[F.sub.n]) of all n-dimensional random vectors X = ([X.sub.1], ..., [X.sub.n]), we have [F.sub.1], ..., [F.sub.n] as marginal distributions, where [F.sub.i](x) := P([X.sub.i] [less than or equal to] x), and the joint distribution function is [mathematical expression not reproducible], we have the following inequality:
Two Sufficient Conditions for Convex Ordering on Risk Aggregation
As [C.sub.k](Y) is a Frechet space, the Open Mapping Theorem [11, Theorem 14.4.6] implies that T : [C.sub.k](Y) [right arrow] [C.sub.k](X) is open, and hence it is a quotient map.
Free Subspaces of Free Locally Convex Spaces
Let X be a Frechet space with a family of seminorms [mathematical expression not reproducible] such that
On a System of Volterra Type Hadamard Fractional Integral Equations in Frechet Spaces
In order to define the "multiplicity" in this generality, we recall that, associated to a continuous representation [pi] of a Lie group on a Banach space H, a continuous representation [[pi].sup.[infinity]] is defined on the Frechet space [H.sup.[infinity]] of [C.sup.[infinity]]-vectors of H.
Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups O(p, q)
We denote by [C.sup.[infinity]]([C.sup.n]) the Frechet space of complex-valued functions on [C.sup.n] endowed with the compact-open topology, while [L.sup.2]([C.sup.n],dm) denotes the usual Hilbert space of square integrable complex-valued functions F(z) on [C.sup.n] with respect to the usual Lebesgue measure dm.
On Concrete Spectral Properties of a Twisted Laplacian Associated with a Central Extension of the Real Heisenberg Group
Therefore, by the Banach-Steinhaus theorem for Frechet space [35], we deduce that [[PI].sub.k] is equally a continuous linear operator on E, and the theorem is established.
Basic Sets of Special Monogenic Polynomials in Frechet Modules
Another way to understand this definition is the following: we choose a pre-Hilbert norm on the Frechet space F.
The Mean Value for Infinite Volume Measures, Infinite Products, and Heuristic Infinite Dimensional Lebesgue Measures
If [LAMBDA] = [R.sub.>0] we can assume that all occurring limits are countable and so [[epsilon].sub.(M)] (U, [R.sup.s]) is a Frechet space. Moreover [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a Silva space, i.e.
The convenient setting for ultradifferentiable mappings of Beurling- and Roumieu-type defined by a weight matrix
It is well known that, if X is a Banach space, then C([R.sub.+]; X) can be organized in a canonical way as a Frechet space, i.e., as a complete metric space in which the corresponding topology is induced by a countable family of seminorms.
A Viscoelastic Contact Problem with Adhesion and Surface Memory Effects
It is well known that A (D) is a Frechet space. By [J.sub.[alpha]] we shall denote the integration operator in the space A(D) defined by the formula
On some operator equations in the space of analytic functions and related questions/Monedest operaatorvorranditest analuutiliste funktsioonide ruumis
In the microlocal analysis we deal with the space of symbols which are infinitely differentiable functions and make it into Frechet space by means of seminorms [5].
Super Weyl transform and some of its properties

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