Displaying similar documents to “Characterizing algebras of C ∞ -functions on manifolds”

A geometric approach to full Colombeau algebras

R. Steinbauer (2010)

Banach Center Publications

Similarity:

We present a geometric approach to diffeomorphism invariant full Colombeau algebras which allows a particularly clear view of the construction of the intrinsically defined algebra ^ ( M ) on the manifold M given in [gksv].

Vector integral equations with discontinuous right-hand side

Filippo Cammaroto, Paolo Cubiotti (1999)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We deal with the integral equation u ( t ) = f ( ∫ I g ( t , z ) u ( z ) d z ) , with t ∈ I = [ 0 , 1 ] , f : 𝐑 n → 𝐑 n and g : I × I → [ 0 , + ∞ [ . We prove an existence theorem for solutions u ∈ L ∞ ( I , 𝐑 n ) where the function f is not assumed to be continuous, extending a result previously obtained for the case n = 1 .

Schwartz kernel theorem in algebras of generalized functions

Vincent Valmorin (2010)

Banach Center Publications

Similarity:

A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of G ∞ -generalized functions class are given. A straightforward relationship between the classical and the generalized...

Division algebras that generalize Dickson semifields

Daniel Thompson (2020)

Communications in Mathematics

Similarity:

We generalize Knuth’s construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension 2 s 2 by doubling central division algebras of degree s . Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.