The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying 121 – 140 of 176

Showing per page

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 α ( s , x ) = n 0 α n ( s ) x n , αn : ℂ → ℂ, n ≥ 0, of the first cocycle equation α ( s + t , x ) = α ( s , x ) α t , F ( s , x ) , s , t , ( Co 1 ) 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 F ( s + t , x ) = F ( s , F ( t , x ) ) , s , t , ( T ) 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 α ( s , x ) = 1 + n 1 α n ( s ) x n are polynomials in ck(s).It is possible to replace...

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 ( f ( x / n ) f ( y / n ) ) .

On the functional equation H [tau (F,G), chi (F,G)] = H (F,G).

Mónica Sánchez Soler (1988)

Stochastica

In this paper we solve the functional equationH [tau(F,G), chi (F,G)] = H (F,G)where the unknowns tau and chi are two semigroups on a space of distribution functions, and H is a given pointwise binary operation on this space satisfying some regularity conditions.

Currently displaying 121 – 140 of 176