منابع مشابه
Additive Polynomials over Perfect Fields
where aij ∈ K. Additive polynomials over valued fields in positive characteristic play an important role in understanding many algebraic and model theoretic properties of maximal fields of positive characteristic, see [7] for a thorough examination of the issue. A subset S of a valued field (K, v) has the optimal approximation property if for all a ∈ K, the set {v(s − a) : s ∈ S} has a maximal ...
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Let A be a C*-algebra which has no quotient isomorphic to M2(C). We show that for every orthogonally additive scalar nhomogeneous polynomials P on A such that P is Strong* continuous on the closed unit ball of A, there exists φ in A∗ satisfying that P (x) = φ(x), for each element x in A. The vector valued analogue follows as a corollary.
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This paper presents a new fast sound synthesis method using polynomials. This is an additive method, where polynomials are used to approximate sine functions. Traditional additive synthesis requires each sample to be generated for each partial oscillator. Then all these partial samples are summed up to obtain the resulting sound sample, thus making the synthesis time proportional to the product...
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If K is a field with discrete valuation ν and D = {a ∈ K : ν(a) ≥ 0}, then an algebra D[x] ⊆ A ⊆ K[x] has associated to it a sequence of fractional ideals {In : n = 0, 1, 2, . . . } with In consisting of 0 and the leading coefficients of elements of A of degree no more than n and a sequence of integers {a(n) : n = 0, 1, 2, . . . } with a(n) = −ν(In). Combinatorial properties of this integer seq...
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We show that, for every orthogonally additive homogeneous polynomial P on a space of continuous functions C(K) with values in a Banach space Y , there exists a linear operator S : C(K) −→ Y such that P (f) = S(f). This is the C(K) version of a related result of Sundaresam for polynomials on Lp spaces.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1955
ISSN: 0002-9947
DOI: 10.2307/1992957