In a recent work of the author, de Branges space was constructed, as well an operator on it whose spectrum coincides with set nontrivial zeros Riemann zeta function after rotation complex plane. Also canonical system related to in question constructed. this paper, natural factorization is exhibited for unitary that realizes correspondence between Hilbert and space, superposition four operators....

Let M be a C-minimal structure and T its canonical tree (which corresponds in an ultrametric space to the set of closed balls with radius different than ∞ ordered by inclusion). We present a description of definable locally constant functions f : M → T in C-minimal structures having a canonical tree with infinitely many branches at each node and densely ordered branches. This provides both a de...

We approach the theory of wavelets from the theory of functional Hilbert spaces. Starting with a Hilbert space H, we consider a subset V of H, for which the span is dense in H. We define a function of positive type on the index set I which labels the elements of V . This function of positive type induces uniquely a functional Hilbert space, which is a subspace of CI and there exists a unitary m...