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Full-Text Articles in Physical Sciences and Mathematics
Invariant Subspaces And Hyper-Reflexivity For Free Semigroup Algebras, Kenneth R. Davidson, David R. Pitts
Invariant Subspaces And Hyper-Reflexivity For Free Semigroup Algebras, Kenneth R. Davidson, David R. Pitts
Department of Mathematics: Faculty Publications
In this paper, we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras. This enables us to prove that they are reflexive, and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces. Such algebras are called hyper-reflexive. This property is very strong, but it has been established in only a very few cases. Moreover the prototypes of this class of algebras are the natural candidate for a non-commutative analytic Toeplitz algebra on n variables. The case we make …
Convolution And Fourier-Feynman Transforms, Chull Park, David Skough
Convolution And Fourier-Feynman Transforms, Chull Park, David Skough
Department of Mathematics: Faculty Publications
In this paper, for a class of funtionals on Wiener space of the form F(x) = exp{∫T0 f(t, x(t)) dt}, we show that the Fourier-Feynman transform of the convolution product is a product of Fourier-Feynman transforms. This allows us to compute the transform of the convolution product without computing the convolution product.
The Nordstrom–Robinson Code Is Algebraic-Geometric, Judy L. Walker
The Nordstrom–Robinson Code Is Algebraic-Geometric, Judy L. Walker
Department of Mathematics: Faculty Publications
The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite field since the early 1980’s. Recently, there has been an increased interest in the study of linear codes over finite rings. In a previous paper [10], we combined these two approaches to coding theory by introducing and studying algebraic-geometric codes over rings. In this correspondence, we show that the Nordstrom–Robinson code is the image under the Gray mapping of an algebraic geometric code over Z = 4Z.