Sine Subtraction Laws on Semigroups

• Autorzy: Bruce Ebanks
• Języki publikacji: EN

Abstrakty

EN

We consider two variants of the sine subtraction law on a semi-groupS. The main objective is to solvef(xy∗) =f(x)g(y)-g(x)f(y)forunknown functionsf,g:S→C, wherex7→x∗is an anti-homomorphic invo-lution. Until now this equation was not solved even whenSis a non-Abeliangroup andx∗=x-1. We find the solutions assuming thatfis central. A sec-ondary objective is to solvef(xσ(y)) =f(x)g(y)-g(x)f(y), whereσ:S→Sis a homomorphic involution. Until now this variant was solved assuming thatShas an identity element. We also find the continuous solutions of these equa-tions on topological semigroups.(original abstract)

Słowa kluczowe

EN

Mathematics; Functional equation

PL

Matematyka; Równanie funkcyjne

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2023
• Tom: 37 (1)
• Strony: 49--66

Twórcy

autor

Bruce Ebanks

• University of Louisville, Louisville, Kentucky, USA

Bibliografia

• Aczél J. and Dhombres J., Functional Equations in Several Variables. With Applications to Mathematics, Information Theory and to the Natural and Social Sciences, Encyclopedia of Mathematics and its Applications, 31, Cambridge University Press, Cambridge, 1989.
• Ebanks B., The cosine and sine addition and subtraction formulas on semigroups, Acta Math. Hungar. 165 (2021), no. 2, 337-354.
• Ebanks B., Around the sine addition law and d'Alembert's equation on semigroups, Results Math. 77 (2022), no. 1, Paper No. 11, 14 pp.
• Ebanks B. and H. Stetkær, d'Alembert's other functional equation on monoids with an involution, Aequationes Math. 89 (2015), no. 1, 187-206.
• Stetkær H., Functional Equations on Groups, World Scientific, Singapore, 2013.
• Stetkær H., Extensions of the sine addition law on groups, Aequationes Math. 93 (2019), no. 2, 467-484.
• Stetkær H., Homomorphisms of product semigroups, Results Math. 77 (2022), no. 2, Paper No. 60, 21 pp.
• Wilson W.H., On certain related functional equations, Bull. Amer. Math. Soc. 26 (1920), no. 7, 300-312.

Identyfikatory

DOI

0.2478/amsil-2023-0002