Search results for "Reciprocal polynomial"

showing 6 items of 6 documents

Periodic Polynomial Splines

2018

In this chapter, the spaces of periodic polynomial splines and the Spline Harmonic Analysis (SHA) in these spaces are briefly outlined. The stuff of this chapter is used for the design of periodic discrete-time splines and discrete-time-spline-based wavelets and wavelet packets. For a detailed description of the subject we refer to (Averbuch, Neittaanmaki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Springer, Berlin, 2014) [1]. Periodic polynomial splines provide an example of mixed discrete-continuous circular convolution.

AlgebraSpline (mathematics)Reciprocal polynomialComputer Science::GraphicsBox splineWaveletComputer scienceSpline waveletCircular convolutionMonic polynomialMathematics::Numerical AnalysisMatrix polynomial
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The maximal coefficient of ternary cyclotomic polynomials with one free prime

2014

A cyclotomic polynomial Φn(x) is said to be ternary if n = pqr, with p, q and r distinct odd primes. Let M(p, q) be the maximum (in absolute value) coefficient appearing in the polynomial family Φpqr(x) with p < q < r, p and q fixed. Here a stronger version of the main conjecture of Gallot, Moree and Wilms regarding M(p, q) is established. Furthermore it is shown that there is an algorithm to compute M(p): = max {M(p, q): q > p}. Our methods are the most geometric used so far in the study of ternary cyclotomic polynomials.

Discrete mathematicsReciprocal polynomialPolynomialAlgebra and Number TheoryAbsolute value (algebra)Ternary operationCyclotomic polynomialPrime (order theory)Mathematics
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Multialternating graded polynomials and growth of polynomial identities

2012

Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by mean of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non vanishing on A. As a consequence we compute the exponential rate of growth of the sequence of graded codimensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. In particular we show it is an integer. The result was proviously known in case G is abelian.

Discrete mathematicsPure mathematicsHilbert series and Hilbert polynomialMathematics::Commutative AlgebraApplied MathematicsGeneral MathematicsMathematics::Rings and AlgebrasGraded ringMathematics - Rings and AlgebrasGraded Lie algebramultialternating polynomialFiltered algebrasymbols.namesakeReciprocal polynomialRings and Algebras (math.RA)Differential graded algebraFactorization of polynomialssymbolsFOS: MathematicsElementary symmetric polynomial16R50 16P90 16R10 16W50Mathematics
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Polynomial numerical indices of 𝐶(𝐾) and 𝐿₁(𝜇)

2013

We estimate the polynomial numerical indices of the spaces C ( K ) C(K) and L 1 ( μ ) L_1(\mu ) .

Reciprocal polynomialAlternating polynomialStable polynomialMinimal polynomial (linear algebra)Applied MathematicsGeneral MathematicsApplied mathematicsMonic polynomialWilkinson's polynomialMathematicsCharacteristic polynomialMatrix polynomialProceedings of the American Mathematical Society
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Polynomial Identities and Asymptotic Methods

2005

Polynomial identities and PI-algebras $S_n$-representations Group gradings and group actions Codimension and colength growth Matrix invariants and central polynomials The PI-exponent of an algebra Polynomial growth and low PI-exponent Classifying minimal varieties Computing the exponent of a polynomial $G$-identities and $G\wr S_n$-action Superalgebras, *-algebras and codimension growth Lie algebras and nonassociative algebras The generalized-six-square theorem Bibliography Index.

Discrete mathematicsPure mathematicsReciprocal polynomialMathematics::Commutative AlgebraSymmetric polynomialStable polynomialAlternating polynomialBracket polynomialMonic polynomialMathematicsMatrix polynomialCharacteristic polynomial
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On the consequences of the standard polynomial

1998

The purpose of this paper is to shed some light on the polynomial identities of low degree for the n × n matrix algebra over a field of characteristic 0.Our main result is that we have found all the consequences of degree n + 2 of the standard polynomial have calculated the S n+2-character of the T-ideal generated by this polynomial.

CombinatoricsDiscrete mathematicsReciprocal polynomialAlgebra and Number TheoryStable polynomialMinimal polynomial (linear algebra)Alternating polynomialDegree of a polynomialMonic polynomialCharacteristic polynomialMathematicsMatrix polynomialCommunications in Algebra
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