By Huntington E.V.

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**Example text**

Thus to define it, we cannot define its value at a point g ∈ G but we can define its restriction to an open neighborhood of g. We will here assume that G ⊂ GL(V ) is a real algebraic group. Then using polar decompositions, we will cover the group G by well adapted neighborhoods in order to give such formulas. Let a ∈ R be a strictly positive real number and let ga be the set of X ∈ g such that the imaginary part Imλ of any eigenvalue λ of the transformation X ∈ End(V ) satisfies |Imλ| < a. Recall that the exponential map is a diffeomorphism of ga on an neighborhood of the identity in G if a is small.

Bott. A Lefschetz fixed-point formula for elliptic complexes: II. Ann. , 88 (1968), 451–491. [3] M. F. Atiyah et F. Hirzebruch. Vector bundles and homogeneous spaces. Amer. Math. Symp. , III (1961), 7–38. [4] M. F. Atiyah et G. B. Segal<. The index of elliptic operators II. Ann. Math. , 87 (1968), 531–545. [5] M. F. Atiyah et I. M. Singer. The index of elliptic operators. I. Ann. Math. , 87 (1968), 484–530. [6] M. F. Atiyah et I. M. Singer. The index of elliptic operators. III. Ann. Math. , 87 (1968), 546–604.

Each element (τ, A) ∈ QG (M, Ω, µ) should give rise to a possible way to quantize the classical Hamiltonian space (M, Ω, µ) in a representation Q(M, τ, A) of G in a Hilbert space H(M, τ, A). Let λ ∈ g∗ . Let H = G(λ) and let M = G/H. 1, we have identified KGt (M ) with K M (H). The map g → g · λ gives us a Hamiltonian structure µ on M (depending on λ ∈ g∗ ). Definition 36 Let X(λ) = {τ ∈ K M (H); τ (exp X) = eiλ(X) I, for X ∈ h}. Recall that in Duflo terminology [23] an orbit G·λ is admissible if X(λ) is non empty.

### An Improved Equal-Frequency Map of the Normal Correlation Surface, Using Circles Instead of Ellipses by Huntington E.V.

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