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On the extension of exponential polynomials

László Székelyhidi (2000)

Mathematica Bohemica

Exponential polynomials are the building bricks of spectral synthesis. In some cases it happens that exponential polynomials should be extended from subgroups to whole groups. To achieve this aim we prove an extension theorem for exponential polynomials which is based on a classical theorem on the extension of homomorphisms.

On the extension of integrable solutions of a functional equation of n-th order

Roman Węgrzyk (1983)

Annales Polonici Mathematici

On the fine spectrum of the generalized difference operator $B (r, s)$ over the sequence spaces $c_{0}$ and $c$ .

Altay, Bilâl, Başar, Feyzi (2005)

International Journal of Mathematics and Mathematical Sciences

On the formal first cocycle equation for iteration groups of type II

Harald Fripertinger, Ludwig Reich (2012)

ESAIM: Proceedings

Let x be an indeterminate over ℂ. We investigate solutions $\begin{matrix} α (s, x) = \sum_{n \geq 0} α_{n} (s) x^{n}, \end{matrix}$ αn : ℂ → ℂ, n ≥ 0, of the first cocycle equation $\begin{matrix} α (s + t, x) = α (s, x) α (t, F (s, x)), s, t \in, (Co 1) \end{matrix}$ in ℂ [[x]], the ring of formal power series over ℂ, where (F(s,x))s ∈ ℂ is an iteration group of type II, i.e. it is a solution of the translation equation $\begin{matrix} F (s + t, x) = F (s, F (t, x)), s, t \in, (T) \end{matrix}$ of the form F(s,x) ≡ x + ck(s)xk mod xk+1, where k ≥ 2 and ck ≠ 0 is necessarily an additive function. It is easy to prove that the coefficient functions αn(s) of $\begin{matrix} α (s, x) = 1 + \sum_{n \geq 1} α_{n} (s) x^{n} \end{matrix}$ are polynomials in ck(s).It is possible to replace...

On the functional equation.

K. Niino (1981)

Aequationes mathematicae

On the Functional Equation

DONALD GIROD (1973)

Aequationes mathematicae

On the functional equation defined by Lie's product formula

Gerd Herzog, Christoph Schmoeger (2006)

Studia Mathematica

Let E be a real normed space and a complex Banach algebra with unit. We characterize the continuous solutions f: E → of the functional equation $f (x + y) = l i m_{n \to \infty} (f (x / n) f (y / n)) ⁿ$ .