Van Vleck’s functional equation for the sine

Stetkær, Henrik

doi:10.1007/s00010-015-0349-z

Cited by 25 publications

(34 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Stetkaer [7] extends the results of Perkins and Sahoo [6] about equation (1.7) to the case where G is a semigroup and the solutions are not assumed to be abelian. The main purpose of this paper is to extend Stetkaer's results [7,8] to the following generalizations of Van Vleck's functional equation for the sine…”

Section: 1)mentioning

confidence: 57%

“…They are generalizations of Stetkaer' lemmas obtained in [7] for µ = δ z0 , where z 0 is a fixed element in the center of the semigroup S.…”

Section: The Solutions Of the Integral Van Vleck's Functional Equatiomentioning

confidence: 85%

“…The main purpose of this paper is to extend Stetkaer's results [7,8] to the following generalizations of Van Vleck's functional equation for the sine…”

Section: 1)mentioning

confidence: 92%

See 2 more Smart Citations

Integral Van Vleck’s and Kannappan’s functional equations on semigroups

Elqorachi

2016

Aequat. Math.

View full text Add to dashboard Cite

Abstract. In this paper we study the solutions of the integral Van Vleck's functional equation for the sineand the integral Kannappan's functional equationwhere S is a semigroup, τ is an involution of S and µ is a measure that is linear combinations of point measures (δz i ) i∈I , such that for all i ∈ I, z i is contained in the center of S. We express the solutions of the first equation by means of multiplicative functions on S, and we prove that the solutions of the second equation are closely related to the solutions of the classic d'Alembert's functional equation with involution.

show abstract

Section: 1)mentioning

confidence: 57%

“…They are generalizations of Stetkaer' lemmas obtained in [7] for µ = δ z0 , where z 0 is a fixed element in the center of the semigroup S.…”

Section: The Solutions Of the Integral Van Vleck's Functional Equatiomentioning

confidence: 85%

See 1 more Smart Citation

Integral Van Vleck’s and Kannappan’s functional equations on semigroups

Elqorachi

2016

Aequat. Math.

View full text Add to dashboard Cite

show abstract

“…Stetkaer [6] extends the results of Perkins and Sahoo [4] about equation (1.4) to the more general case where G is a semigroup and the solutions are not assumed to be abelian. The first purpose of this paper is to extend the results of Stetkaer [6] to the following generalization of Van Vleck's functional equation for the sine…”

Section: Introductionmentioning

confidence: 55%

“…The first purpose of this paper is to extend the results of Stetkaer [6] to the following generalization of Van Vleck's functional equation for the sine…”

Section: Introductionmentioning

confidence: 98%