Abstract The classical Gleason-Kahane-Żelazko Theorem states that a linear functional on complex Banach algebra not vanishing units, and such $$\Lambda (\textbf{1})=1$$ Λ ( 1 ) = , is multiplicative, is, (ab)=\Lambda (a...

We prove that, after removing a zero Hausdorff dimension exceptional set of parameters, all self-similar measures on the line have power decay Fourier transform at infinity. In homogeneous case, when contraction ratios are equal, this is essentially due to Erdős and Kahane. non-homogeneous case difficulty we overcome apparent lack convolution structure.

Abstract The main aim of this work is to discuss several different approaches the celebrated Kahane–Salem–Zygmund inequalities. In particular, we prove estimates for exponential Orlicz norms averages $$\sup _{1\le j\le N}\Big |\sum _{i=1}^K a_i(j) \gamma _i\Big |\,,$$ sup 1 ...

The only description of extractions in TAG we know has been developed by Kroch & Joshi (1986), Kroch (1987) and implemented in the developed grammars of English (XT AG 1995) and French (Abeille 1991, Candito 1999). This implementation sol ves the unboundedness of extractions with predicative adjoining, but the pied-piping is solved using a special feature. We think that this solution of pied-pi...

A well-known theorem of Zygmund (6) states that if n 1 < n 2 <. .. is a sequence of integers satisfying a (1) n~ +i/n~ > l+c (c > 0), k=1 converges for at least one x ; in fact the set of x for which (2) converges is of power c in any interval. Paley and Mary Weiss (5) extended this theorem for power series, i .e. (3) Y a i.znk k=1 converges for at least one z with I z I = 1 ; in fact the set o...

We establish the following Hilbert-space analogue of Gleason-Kahane-\.Zelazko theorem. If $\mathcal{H}$ is a reproducing kernel Hilbert space with normalized complete Pick kernel, and if $\Lambda$ linear functional on such that $\Lambda(1)=1$ $\Lambda(f)\ne0$ for all cyclic functions $f\in\mathcal{H}$, then multiplicative, in sense $\Lambda(fg)=\Lambda(f)\Lambda(g)$ $f,g\in\mathcal{H}$ $fg\in\m...