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We develop a theory of almost periodic elements in Banach algebras and present an abstract version of anoncommutative Wiener’s Lemma. The theory can be used, for example, to derive some of the recentl...
In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracia...
To calibrate Fourier analysis of S5 ranking data by Markov chain Monte Carlo techniques, a set of moves (Markov basis) is needed. We calculate this basis, and use it to provide a new statistical analy...
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are relate...
If X is a compact Hausdorff space, supplied with a homeomorphism, then a crossed product involutive Banach algebra is naturally associated with these data. If X consists of one point, then this algebr...
We study rational actions of an algebraic torus G by automorphisms on an associative algebra R. The G-action on R induces a stratification of the prime spectrum of R which was introduced by Goodearl a...
We describe noncommutative desingularizations of determinantal varieties, determinantal varieties defined by minors of generic symmetric matrices, and pfaffian varieties defined by pfaffians of generi...
We study perturbations of the flat geometry of the noncommutative two-dimensional torus T^2_\theta (with irrational \theta). They are described by spectral triples (A_\theta, \H, D), with the Dirac op...
We study the Chern-Simons action, which was defined for noncommutative spaces in general by the author, for the noncommutative 3-torus, the universal C*-algebra generated by 3 unitaries. D. Essouabri,...
Witten constructed a topological quantum field theory with the Chern-Simons action as Lagrangian. We define a proper noncommutative generalization of the Chern-Simons action. "Proper", in this context...
The paper introduces the concept of noncommutative Banach spaces and obtains several fixed point theorems for continuous or discontinuous ordered contractive maps in ordered noncommutative Banach spac...
We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least as strong as Frege, ...
Abstract: We consider the CSS algorithm relating self-orthogonal classical linear codes to q-ary quantum stabilizer codes and we show that to such a pair of a classical and a quantum code one can asso...
Abstract: We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For...
Abstract: In this paper we construct a version of Ricci flow for noncommutative 2-tori, based on a spectral formulation in terms of the eigenvalues and eigenfunction of the Laplacian and recent result...

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