Functional equations for trigonometric functions

Stability of Trigonometric Functional Equations in Generalized Functions

On the Stability of Trigonometric Functional Equations

On a Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

The Hyers-Ulam stability problems of functional equations go back to 1940 when S. M. Ulam proposed a question concerning the approximate homomorphisms from a group to a metric group see 1 . A partial answer was given by Hyers et al. 2, 3 under the assumption that the target space of the involved mappings is a Banach space. After the result of Hyers, Aoki 4 , and Bourgin 5, 6 dealt with this pro...

‘degeneration of Trigonometric Dynamical Difference Equations for Quantum Loop Algebras to Trigonometric Casimir Equations for Yangians’

We show that, under Drinfeld’s degeneration [D] of quantum loop algebras to Yangians, the trigonometric dynamical difference equations [EV] for the quantum affine algebra degenerate to the trigonometric Casimir differential equations [TL] for Yangians.

Functional Equations for Quantum Theta Functions

Quantum theta functions were introduced by the author in [Ma1]. They are certain elements in the function rings of quantum tori. By definition, they satisfy a version of the classical functional equations involving shifts by the multiplicative periods. This paper shows that for a certain subclass of period lattices (compatible with the quantization form), quantum thetas satisfy an analog of ano...