Revised assignment of olefinic proton signals in the 1H-NMR spectra of dienoid-type erythrinan alkaloids
Previous assignment of the olefinic proton signals (H-1 and H-2) in the 1 H-nmr spectra of dienoid-type erythrinan alkaloids was interchanged on the basis of the synthesis of the stereoisomers, nOe experiments, and theoretical calculations
In this paper we study the multivariate ANOVA decomposition for $1$-periodic functions on the torus. In particular we use the integral projection operator that leads to the classical ANOVA decomposition. Relationships between the Fourier coefficients of the function and its ANOVA terms lead to special frequency index sets and give an understanding of the decomposition working in the frequency domain. Moreover, we consider the truncated ANOVA decomposition and provide error bounds for approximation in $\mathrm{L}_\infty$ and $\mathrm{L}_2$. We present an approximation method based on the truncated decomposition with regard to a superposition dimension $d_s$.