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Full-Text Articles in Physical Sciences and Mathematics
Absolutely Continuous Representations And A Kaplansky Density Theorem For Free Semigroup Algebras, Kenneth R. Davidson, Jiankui Li, David R. Pitts
Absolutely Continuous Representations And A Kaplansky Density Theorem For Free Semigroup Algebras, Kenneth R. Davidson, Jiankui Li, David R. Pitts
Department of Mathematics: Faculty Publications
We introduce notions of absolutely continuous functionals and representations on the non-commutative disk algebra An. Absolutely continuous functionals are used to help identify the type L part of the free semigroup algebra associated to a ∗-extendible represen- tation . A ∗-extendible representation of An is regular if the absolutely continuous part coincides with the type L part. All known examples are regular. Absolutely continuous func- tionals are intimately related to maps which intertwine a given ∗-extendible representation with the left regular representation. A simple application of these ideas extends reflexivity and hyper-reflexivity results. Moreover the use of absolute continuity is …
Integral Transforms, Convolution Products, And First Variations, Bong Jin Kim, Byoung Soo Kim, David Skough
Integral Transforms, Convolution Products, And First Variations, Bong Jin Kim, Byoung Soo Kim, David Skough
Department of Mathematics: Faculty Publications
We establish the various relationships that exist among the integral transform Fα,βF, the convolution product (F∗G)α, and the first variation δF for a class of functionals defined on K[0,T], the space of complex-valued continuous functions on [0,T] which vanish at zero.
A Survey Of Results Involving Transforms And Convolutions In Function Space, David Skough, David Storvick
A Survey Of Results Involving Transforms And Convolutions In Function Space, David Skough, David Storvick
Department of Mathematics: Faculty Publications
In this paper we survey various results involving Fourier-Wiener transforms, Fourier-Feynman transforms, integral transforms and convolution products of functionals over function space that have been established since Cameron and Martin first introduced Fourier-Wiener transforms in 1945.