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Let G be a locally compact abelian group and G < sup >^</ sup > be the Pontryagin dual of G. The Fourier-Plancherel transform defined by
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Let and G
Suppose that in a mathematical language L, it is possible to enumerate all of the defined numbers in L. Let this enumeration be defined by the function G: W → R, where G ( n ) is the real number described by the nth description in the sequence.
Let G denote the set of bijective functions over A that preserve the partition structure of A: ∀ x ∈ A ∀ g ∈ G ( g ( x ) ∈ ).
Moving to groups in general, let H be a subgroup of some group G. Let ~ be an equivalence relation on G, such that a ~ b ↔ ( ab < sup >− 1 </ sup > ∈ H ).
Let G be a set and let "~" denote an equivalence relation over G. Then we can form a groupoid representing this equivalence relation as follows.
Let E be the intersection of the diagonals, and let F be on side DA and G be on side BC such that FEG is parallel to AB and CD.
Let F and G be a pair of adjoint functors with unit η and co-unit ε ( see the article on adjoint functors for the definitions ).
Let and be
Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.
Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.
Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.
Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.
Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.
Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.
Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.
Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.
Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.
Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.
Let and locally
Let X be a locally compact Hausdorff space equipped with a finite Radon measure μ, and let Y be a σ-compact Hausdorff space with a σ-finite Radon measure ρ.
Let X be locally ringed space with structure sheaf O < sub > X </ sub >; we want to define the tangent space T < sub > x </ sub > at the point x ∈ X.
Let be a connected and locally connected based topological space with base point x, and let be a covering with fiber.
Let X be a smooth projective variety where all of its irreducible components have dimension n. Then one has the following version of the Serre duality: for any locally free sheaf on X,
The locally quarried sandstone building displays a stylised sun with a carved motto-" Let there be light " at the entrance.
Let e =( e < sub > α </ sub >)< sub > α = 1, 2 ,..., k </ sub > be a local frame on E. This frame can be used to express locally any section of E. For suppose that ξ is a local section, defined over the same open set as the frame e, then
To push for more support locally, the club planted the slogan ' Let Arsenal support Islington ' around Highbury during matches against Aston Villa and Juventus in December 2001 and as a backdrop for manager Arsène Wenger's press conference in the lead up to Christmas.
Let G be a σ-compact, locally compact topological group and π: G U ( H ) a unitary representation of G on a ( complex ) Hilbert space H. If ε > 0 and K is a compact subset of G, then a unit vector ξ in H is called an ( ε, K )- invariant vector if π ( g ) ξ-ξ < ε for all g in K.
Let H be a topological group and let G be a covering space of H. If G and H are both path-connected and locally path-connected, then for any choice of element e * in the fiber over e ∈ H, there exists a unique topological group structure on G, with e * as the identity, for which the covering map p: G → H is a homomorphism.
Let S be a locally compact second countable Hausdorff space equipped with its Borel σ-algebra B ( S ).
Let C be a locally small category ( i. e. a category for which hom-classes are actually sets and not proper classes ).
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