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Content available remote Fourier analysis on locally convex spaces of distributions, II
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This is the second in a series of papers, extending the theory of Fourier analysis to locally convex spaces of distributions (LCD-spaces). In this paper, LCD-spaces admitting conjugation and multiplier operators on LCD-spaces are discussed. It is also shown that if E is an LCD-space having C∞ as a dense subset, then E*, endowed with the topology of precompact convergence, is an LCD-space having C∞ as a dense subset.
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Content available remote Fourier analysis on locally convex spaces of distributions, I
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EN
In this series of papers, many results of Fourier analysis which are known for Lp (1 < p < oo) , C (the space of continuous functions) and other Banach spaces of functions have been generalized to locally convex spaces of distributions. Also, in this paper, the (C, 1)-complementary space E' of a locally convex space of distributions E is defined and it is shown that E' , as a subspace of E* with strong* topology, is a locally convex space of distributions.
EN
Cyanobacteria are known to biosynthesize mycosporine-like amino acids (MAAs) as photoprotective compounds against ultraviolet radiation. Anabaena sp., isolated from the hot springs of Rajgir, India, produces a single MAA shinorine (retention time = 2.2 min and absorption maximum at 334 nm) as purified by high-performance liquid chromatography. The MAA biosynthesis was under constitutive control in this cyanobacterium; however, PAR + UV-A + UV-B radiation was found to have highest impact on MAA synthesis. MAA biosynthesis is dependent on photosynthesis for the carbon source since the inhibitory effect of DCMU on MAA synthesis was overcome by externally added fructose. Our results suggest that there is no direct involvement of photosystem II dependent linear electron transport in MAA biosynthesis. However, utilization of energy derived from photosystem I dependent cyclic electron transport in MAA biosynthesis cannot be ruled out. This study also reveals that photoheterotrophic growth can support highest MAA biosynthesis under laboratory conditions in comparison with photoautotrophic and photomixotrophic growth. Thus, photoheterotrophic growth condition can be used for the large-scale production of pharmaceutically important MAAs from cyanobacteria for an industrial application.
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