Displaying similar documents to “Algebras of differentiable functions”

Moebius-invariant algebras in balls

Walter Rudin (1983)

Annales de l'institut Fourier

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It is proved that the Fréchet algebra C ( B ) has exactly three closed subalgebras Y which contain nonconstant functions and which are invariant, in the sense that f ∘ Ψ ∈ Y whenever f ∈ Y and Ψ is a biholomorphic map of the open unit ball B of C n onto B . One of these consists of the holomorphic functions in B , the second consists of those whose complex conjugates are holomorphic, and the third is C ( B ) .

Algebras of differentiable functions in the plane

Karel De Leeuw, H. Mirkil (1963)

Annales de l'institut Fourier

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Soit A un ensemble quelconque d’opérateurs différentiels en deux variables à coefficients complexes constants. Soit C 0 l’espace des fonctions continues complexes tendant vers zéro à l’infini dans le plan euclidien. Soit C 0 ( A ) l’espace { f : f ∈ C 0 , A f C 0 , tout a ∈ A } . Classifier ces espaces équivaut à trouver des conditions nécessaires et suffisantes sur des opérateurs différentiels P 1 , ... , P n pour que ∥ P 1 φ ∥ ∞ ≤ K ( ∥ P 2 φ ∥ ∞ + ⋯ + ∥ P n φ ∥ ∞ ) . Il paraît que ce problème général est bien difficile. Nous présentons ici la solution complète dans le cas spécial des...

On classical invariant theory and binary cubics

Gerald W. Schwarz (1987)

Annales de l'institut Fourier

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Let G be a reductive complex algebraic group, and let C [ m V ] G denote the algebra of invariant polynomial functions on the direct sum of m copies of the representations space V of G . There is a smallest integer n = n ( V ) such that generators and relations of C [ m V ] G can be obtained from those of C [ n V ] G by polarization and restitution for all m > n . We bound and the degrees of generators and relations of C [ n V ] G , extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics. ...

A note on spaces of type H ∞ + C

David Stegenga (1975)

Annales de l'institut Fourier

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We show that a theorem of Rudin, concerning the sum of closed subspaces in a Banach space, has a converse. By means of an example we show that the result is in the nature of best possible.