Open Access. Powered by Scholars. Published by Universities.®
- Keyword
Articles 1 - 3 of 3
Full-Text Articles in Mathematics
Weak Factorizations, Fractions And Homotopies, Alexander Kurz, Jiří Rosický
Weak Factorizations, Fractions And Homotopies, Alexander Kurz, Jiří Rosický
Engineering Faculty Articles and Research
We show that the homotopy category can be assigned to any category equipped with a weak factorization system. A classical example of this construction is the stable category of modules. We discuss a connection with the open map approach to bisimulations proposed by Joyal, Nielsen and Winskel.
Point Evaluation And Hardy Space On A Homogeneous Tree, Daniel Alpay, Dan Volok
Point Evaluation And Hardy Space On A Homogeneous Tree, Daniel Alpay, Dan Volok
Mathematics, Physics, and Computer Science Faculty Articles and Research
We consider stationary multiscale systems as defined by Basseville, Benveniste, Nikoukhah and Willsky. We show that there are deep analogies with the discrete time non stationary setting as developed by the first author, Dewilde and Dym. Following these analogies we define a point evaluation with values in a C*–algebra and the corresponding “Hardy space” in which Cauchy’s formula holds. This point evaluation is used to define in this context the counterpart of classical notions such as Blaschke factors.
Rational Hyperholomorphic Functions In R4, Daniel Alpay, Michael Shapiro, Dan Volok
Rational Hyperholomorphic Functions In R4, Daniel Alpay, Michael Shapiro, Dan Volok
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce the notion of rationality for hyperholomorphic functions (functions in the kernel of the Cauchy-Fueter operator). Following the case of one complex variable, we give three equivalent definitions: the first in terms of Cauchy-Kovalevskaya quotients of polynomials, the second in terms of realizations and the third in terms of backward-shift invariance. Also introduced and studied are the counterparts of the Arveson space and Blaschke factors.