On the Cauchy equation modulo Z

On polynomial congruences

“…In the present paper we obtain results which correspond to those of Baron et al from [2] and results of Baron and Volkmann from [3]. Namely, we present analogues of results from [2,3] for polynomial congruences of degree greater than 1.…”

“…Namely, we present analogues of results from [2,3] for polynomial congruences of degree greater than 1. Below we cite one of the characterizations of decent solutions of the Cauchy's congruence from [2], because we use it in Remark 1.3: When dealing with polynomial functions the inductional approach may always come in mind.…”

On orthogonally exponential functionals

“…, y ∈ U} for n ∈ N. The next proposition and two theorems correspond to the results contained in [4], [6] and [7]. Proposition 2.4.…”

“…Let X be a real topological linear space, (G, +) be a commutative topological group without elements of order 2, K be a discrete subgroup of G, and f : X → G be a continuous at the origin function satisfying (6). Then 2f (0) ∈ K and there is a unique quadratic function q : X → G, continuous at the origin, such that (7) holds.…”

“…Let X and W be just the same as in Lemma 2.3. Suppose that (G, +) is a commutative group without elements of order 2, K is a subgroup of G, U = ∅ is a subset of G with U = −U and U (6) …”