Beispiele von Pseudo-Differentialoperator-Algebrenfl

Discussion of methods in theory of Partial Differential Operators (and Pseudo-Differential Operators) which are based on Gel'fand theory of commutative Banach Algebras. These methods all are discussed for the (non-compact) manifold Rⁿ, for L^p/-SobolefF spaces W_p,k (including k = ∞) and for operators of "Laplace-type", which, crudely, amounts to "elliptic type". Generalizations to general non-compact manifolds and to hypo-elliptic operators have been worked out in detail in [6], for example. Two types of symbol are introduced for a (Pseudo)-differential operator: the Laplace-symbol-quotient ^s (of order s) and the symbol σ. Among the results we have (a) necessary and sufficient criteria for the existence of an W^:p,-Fredholm inverse, (b) essential self-adjointness and (c) characterization of the essential spectrum of elliptic (Pseudo-) Differential operators.     

Konvergenz in verallgemeinerten topologischen Räumen

Spline – projectors in BANACH spaces. A class of BANACH spaces is studied in which it is possible to construct explicitly spline – projectors. These projectors do not depend on the special HILBERT structure that is used for construction; therefore they are unique determined.     

Zur Einbettung von Inzidenzräumen und angeordneten Räumen

We characterize subsets of incidence spaces, which are locally complete resp. bundletrue (bündeltreu). Then we specify necessary and sufficient conditions to extend the embedding of a subset of a space into another space to an embedding of the complete space. Using these results we show that every ordered space (not necesserily fulfilling (O3), cf. §4) can be embedded into a projective space. The last result is a generalization of former results using the additional assumption (O3) (cf. [2,9,10]).     

Beispiele zur Differentialtopologie von Singularitäten

Ohne ZusammenfassungThis Research was supported by Air Force Office of Scientific Research gran A-AFOSR 335-63.