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

A geometric approach to full Colombeau algebras

R. Steinbauer (2010)

Banach Center Publications

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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

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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

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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...

On Boman's theorem on partial regularity of mappings

Tejinder S. Neelon (2011)

Commentationes Mathematicae Universitatis Carolinae

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Let Λ ⊂ ℝ n × ℝ m and k be a positive integer. Let f : ℝ n → ℝ m be a locally bounded map such that for each ( ξ , η ) ∈ Λ , the derivatives D ξ j f ( x ) : = d j d t j f ( x + t ξ ) | t = 0 , j = 1 , 2 , ⋯ k , exist and are continuous. In order to conclude that any such map f is necessarily of class C k it is necessary and sufficient that Λ be not contained in the zero-set of a nonzero homogenous polynomial Φ ( ξ , η ) which is linear in η = ( η 1 , η 2 , ⋯ , η m ) and homogeneous of degree k in ξ = ( ξ 1 , ξ 2 , ⋯ , ξ n ) . This generalizes a result of J. Boman for the case k = 1 . The statement and the proof of a theorem of Boman for the case k = ∞ is...

Generalized Post algebras and their application to some infinitary many-valued logics

Cat-Ho Nguyen

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CONTENTSIntroduction............................................................................................................................................................................... 5Part I. A generalization of Post algebras............................................................................................................................. 7   1. Definition and characterization of generalized Post algebras............................................. 7   2. Post...