منابع مشابه
Harmonic Analysis on Vector Spaces over Finite Fields
• (i) G = ZN = Z/NZ = {0, 1, 2, ....., N − 1} with addition modulo N . For 0 ≤ n ≤ N − 1 let γn : G → S, γn(m) = exp(2πimn/N). Then {γ0, ....., γN−1} is a complete list of the characters so that ZN is isomorphic to ZN . An example of a primitive N ’th root of unity is ω := exp 2πi/N . • (ii) G = T = R/Z; for n ∈ Z let γn : G→ S, γn(x) = exp(2πinx). Then G∗ = {γn : n ∈ Z} so that G∗ is isomorphi...
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The Galois number Gn(q) is defined to be the number of subspaces of the n-dimensional vector space over the finite field GF (q). When q is prime, we prove that Gn(q) is equal to the number Ln(q) of n-dimensional mod q lattices, which are defined to be lattices (that is, discrete additive subgroups of n-space) contained in the integer lattice Z and having the property that given any point P in t...
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Let G be a reductive group in the Harish-Chandra class e.g. a connected semisimple Lie group with finite center, or the group of real points of a connected reductive algebraic group defined over R. Let σ be an involution of the Lie group G, H an open subgroup of the subgroup of fixed points of σ. One decomposes the elements of L(G/H) with the help of joint eigenfunctions under the algebra of le...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1970
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1970-0301162-2