A class of multidimensional periodic splines

Periodic spline functions are introduced by use of reproducing kernel structure in Hilbert spaces. Minimum properties are described in interpolation and best approximation problems. A numerical method for determining interpolating splines and best approximations is proposed.Dedicated to Prof. Dr. F. Reutter on the occasion of his 70th birthday     

Die Automorphismen der isotropen Bewegungsgruppe

Ohne ZusammenfassungHerrn Professor K.Strubecker zum 60. Geburtstag     

Conjugate function theory in weak1 Dirichlet algebras

The fundamental theorems on conjugate functions are shown to be valid for weak¹ Dirichlet algebras. In particular the conjugation operator is shown to be a continuous map of L^p to L^p for 1 < p < ∞, to be a continuous map of L¹ to L^p, 0 < p < 1, and to map functions in L^∞ to exponentially integrable functions. These results allow a number of results for Dirichlet algebras to be extended to weak¹ Dirichlet algebras.     

Gauge fields,BRS symmetry and the Casimir effect

The canonical quantization of the photon field in covariant gauge is studied in the presence of static boundaries, on which the field satisfies either “bag” or superconductor boundary conditions. The inclusion of the Fadeev-Popov ghost fields is found to be essential for agreement with Coulomb gauge calculations of the Casimir energy.     

Synthesis of des-n-tetramethyltriostin a from C-terminal Z-d-serine tetra-and octadepsipeptide intermediates

Des-N-tetramethyltriostin A (1), a known DNA-intercalation agent, has been synthesized from tetra- and octapeptide intermediates that have Z-d-serine at the C-terminal position. The procedure thus allows the fragment coupling and cyclization reactions leading to the synthesis of the title compound to occur without racemization at the C-terminal amino acid. Esterification of Boc-Val-OH with the p-bromophenacyl ester of Z-d-serine provided didepsipeptide Z-d-Ser(Boc-Val)-OBpa (4). Stepwise addition of the requisite amino acids provided tetradepsipeptide Z-d-Ser[Boc-Ala-Cys(Acm)-Val]-OBpa (6). Fragment coupling of the respective C- and N-deprotected tetradepsipeptides 7 and 8, derived from 6, furnished linear octadepsipeptide 9, which upon cyclization and disulfide formation gave the bicyclic octadepsipeptide 11, a known synthetic precursor to 1. The degree of racemization incurred in the alanine and valine residues of selected depsipeptides was measured and the results compared with those obtained in previous studies. It was concluded that alanine, perhaps because of sequence effects, undergoes a degree of racemization (4–10%) during hydrolysis of tetradepsipeptide 6 and octadepsipeptide 9.