Abstract
In the present paper we characterize the solutions of each of the integral functional equations
where G is a locally compact Hausdorff group, \(\sigma :G\rightarrow G\) is a continuous homomorphism such that \(\sigma \circ \sigma =I,\) and \(\mu \) is a regular, compactly supported, complex-valued Borel measure on G.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aczél, J.: Lectures on Functional Equations and Their Applications. Mathematics in Science and Engineering, vol. 19. Academic Press, New York (1966)
Akkouchi, M., Bakali, A., Khalil, I.: A class of functional equations on a locally compact group. J. Lond. Math. Soc. 57(2), 694–705 (1998)
Chung, J.K., Kannappan, P., Ng, C.T.: A generalization of the cosine-sine functional equation on groups. Linear Algebra Appl. 66, 259–277 (1985)
Ebanks, B.R., Stetkær, H.: d’Alembert’s other functional equation on monoids with an involution. Aequat. Math. 89, 187–206 (2015)
Elqorachi, E., Redouani, A.: Trigonometric formulas and \( \mu \)-spherical functions. Aequat. Math. 72, 60–77 (2006)
Fadli, B., Zeglami, D., Kabbaj, S.: Generalized Van Vleck’s equation on locally compact groups. Proyecc. J. Math. 36(4), 545–566 (2017)
Gajda, Z.: A generalization of d’Alembert’s functional equation. Funkc. Ekvacioj 33, 69–77 (1990)
Kannappan, P.: Functional Equations and Inequalities with Applications. Springer, New York (2009)
Poulsen, T.A., Stetkær, H.: On the trigonometric subtraction and addition formulas. Aequat. Math. 59(1–2), 84–92 (2000)
Stetkær, H.: Trigonometric functional equations of rectangular type. Aequat. Math. 56(3), 251–270 (1998)
Stetkær, H.: Functional Equations on Groups. World Scientific Publishing Company, Singapore (2013)
Stetkær, H.: The cosine addition law with an additional term. Aequat. Math. 90(6), 1147–1168 (2016)
Stetkær, H.: Kannappan’s functional equation on semigroups with involution. Semigroup Forum 94(1), 17–30 (2017)
Stetkær, H.: Van Vleck’s functional equation for the sine. Aequat. Math. 90(1), 25–34 (2016)
Székelyhidi, L.: Convolution Type Functional Equations on Topological Abelian Groups. World Scientific Publishing Company, Singapore (1991)
Van Vleck, E.B.: A functional equation for the sine. Ann. Math. Second Ser. 11(4), 161–165 (1910)
Zeglami, D., Kabbaj, S., Charifi, A., Roukbi, A.: \(\mu \)-Trigonometric functional equations and Hyers-Ulam stability problem in hypergroups, functional equations in mathematical analysis. In: Springer Optimization and Its Applications, vol. 52, p. 6 (2012). https://doi.org/10.1007/978-1-4614-0055-4
Zeglami, D., Fadli, B., Kabbaj, S.: Harmonic analysis and generalized functional equations for the cosine. Adv. Pure Appl. Math. 7(1), 41–49 (2016)
Zeglami, D., Fadli, B.: Integral functional equations on locally compact groups with involution. Aequat. Math. 90, 967–982 (2016)
Zeglami, D.: Some functional equations related to number theory. Acta Math. Hungar. 149(2), 490–508 (2016)
Zeglami, D., Tial, M., Kabbaj, S.: The integral sine addition law, Proyecc. J. Math. (Submitted)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kabbaj, S., Tial, M. & Zeglami, D. The Integral Cosine Addition and Sine Subtraction Laws. Results Math 73, 97 (2018). https://doi.org/10.1007/s00025-018-0858-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00025-018-0858-x