Spectral properties of operators of the theory of harmonic potential

We classify the points of the spectrum of the operatorsB andB ^* of the theory of harmonic potential on a smooth closed surfaceS ³. These operators give the direct value onS of the normal derivative of the simple layer potential and the double layer potential. We show that zero can belong to the point spectrum of both operators inL ₂ (S). We prove that the half-interval [–2, 2) is densely filled by spectrum points of the operators for a varying surface; this is a generalization of the classical result of Plemelj. We obtain a series of new spectral properties of the operatorsB andB ^* on ellipsoidal surfaces.Translated fromMatematicheskie Zametki, Vol. 59, No. 1, pp. 3–11, January, 1996.This research was partially supported by the Russian Foundation for Basic Research.     

Galloyl-Derived Orthoquinones as Reactive Partners in Nucleophilic Additions and Diels-Alder Dimerizations: A Novel Route to the Dehydrodigalloyl Linker Unit of Agrimoniin-Type Ellagitannins

Orthochloranil-mediated oxidation of galloyl monoethers furnishes the derived orthoquinones in excellent yield. These reactive electrophiles participate in a variety of nucleophilic addition reactions with heteroatomic and carbanionic partners. In addition, Lewis acid-mediated dimerization of the orthoquinones provides an efficient route to dehydrodigalloyl-type diaryl ether units characteristic of several ellagitannin natural products. The implications for ellagitannin biosynthesis and gallotannin-protein covalent attachment are discussed.