Despite significant progress over the past decades, all state-of-the-art population synthesis (PS) codes suffer from deficiencies limiting their potential of gaining sharp insights into the star formation history (SFH) and Chemical Enrichment History (CEH) of star-forming galaxies, i.e. the neglect of nebular continuum and, the lack of a mechanism to ensure consistency between the best-fitting SFH and the observed nebular characteristics (ONC; Balmer-lines, Balmer/Paschen jumps). These introduce biases in their recovered physical properties (stellar mass M* and sSFR). FADO is a novel self-consistent PS code employing genetic optimization, publicly available (http://www.spectralsynthesis.org), capable of identifying the SFH & CEH that reproduce the ONC of a galaxy, alleviating degeneracies in the spectral fits. The current version of FADO (v1.b) uses standard BPT emission-line ratios for the classification of low redshift (z) galaxies. Whereas this permits a reliable distinction between star-forming, Composite, Seyfert and LINERs, it is inapplicable to many intermediate-z galaxies. We present an adaptation of FADO (version v1.c) to classify higher z galaxies employing the “Blue Diagram” (e.g., Lamareille 2010) for which the most prominent blue emission-lines (< [OIII]5007Å) are observable while the Hα and [NII] are inaccessible. FADO v1.c was applied to synthetic spectra simulating the evolution of galaxies formed at higher-z with different SFHs. FADO can recover the physical and evolutionary properties of galaxies, such as M* and mean age/metallicity, with an accuracy significantly better than purely-stellar codes. An outline of FADO v1.c and applications to local and intermediate-z galaxies will be presented.

Let G be a locally compact Hausdorif abelian group and X be a complex Banach space. Let C(G, X) denote the space of all continuous functions f: G → X, with the topology of uniform convergence on compact sets. Let X′ denote the dual of X with the weak* topology. Let Mc(G, X′) denote the space of all X′-valued compactly supported regular measures of finite variation on G. For a function f ∈ C(G, X) and μ ∈ Mc(G, X′), we define the notion of convolution f * μ. A function f ∈ C(G, X) is called mean-periodic if there exists a non-trivial measure μ ∈ Mc(G, X′) such that f * μ = 0. For μ ∈ Mc(G, X′), let M P(μ) = {f ∈ C(G, X): f * μ = 0} and let M P(G, X) = ∪μ M P(μ). In this paper we analyse the following questions: Is M P(G, X) ≠ 0? Is M P(G, X) ≠ C(G, X)? Is M P(G, X) dense in C(G, X)? Is M P(μ) generated by ‘exponential monomials’ in it? We answer these questions for the groups G = ℝ, the real line, and G = T, the circle group. Problems of spectral analysis and spectral synthesis for C(ℝ, X) and C(T, X) are also analysed.