On polynomials in additive and multiplicative functions

Reich, Ludwig; Schwaiger, Jens

doi:10.1007/978-94-009-6320-7_12

Cited by 21 publications

(17 citation statements)

References 5 publications

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“…The following result about linear independence of group characters can be compared with Theorem 3, p. 135 of [7] and Theorem 3, p. 73 of [5]. See also [6], Lemma p. 236.…”

Section: General Set Upmentioning

confidence: 92%

On a signed cosine equation ofN summands

Stetkær

1996

Aeq. Math.

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“…The following result about linear independence of group characters can be compared with Theorem 3, p. 135 of [7] and Theorem 3, p. 73 of [5]. See also [6], Lemma p. 236.…”

Section: General Set Upmentioning

confidence: 92%

On a signed cosine equation ofN summands

Stetkær

1996

Aeq. Math.

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“…The aim of this section is to generalize and to sharpen the main result, Theorem 12, of [RS,section 7]. Since there are many misprints in this paper we allow ourselves also to repeat some arguments from there.…”

Section: Polynomials In Additive Functions and Their Characterizationmentioning

confidence: 98%

“…It is a generalization of an example, originally presented in [RS,Section 7], of a generalized polynomial, which is not a polynomial in additive functions. We will derive a contradiction to (A) in two ways, firstly by a result of Section 3 and secondly using results of Section 2 and of the present section.…”

Section: Q(x) + Ci(y) = £(B*(x)) + £(B*(y)) = I ((^ + B*{x)){ei + B*(mentioning

confidence: 99%

Polynomials in Additive Functions and Generalized Polynomials

Schwaiger¹,

Prager²

2008

Demonstratio Mathematica

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Abstract. We consider polynomials P in additive functions gi,... ,g m and present two approaches for a characterization of those generalized polynomials p, which may beUnder rather general assumptions on the domains of the gi and of P, one of the approaches is based on certain properties of subspaces generated by translates of p. The other approach utilizes the fact, that every p is the diagonalization of an associated multi-Jensen function.

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“…Lemma 3], [11,Theorem 6], [21,Lemma 4.3]). In both cases we may use E = E 4 , α = a 1 a 2 γ and β = b 1 b 2 δ .…”

Section: We See That A(y)f (X) = A(−y)f(x) and So A(y) = A(−y) Hencementioning

confidence: 99%

“…So [11]) and applying Lemma 3 to (21) we find ν = 6λφ 2 + 6λ 1 φφ 0 and f 0 = 2λµφ 3 + 3λ 1 µφ 2 φ 0 + µφ 1 .…”

Section: B = B 4 Thenmentioning

confidence: 99%