48 citations · 56 across the 7 of their papers we have counts for
7 papers
Noncommutative Networks on a Cylinder
S. Arthamonov, N. Ovenhouse, M. Shapiro
In this paper a double quasi Poisson bracket in the sense of Van den Bergh is constructed on the space of noncommutative weights of arcs of a directed graph embedded in a disk or c…
Kolmogorov's axioms for probabilities with values in hyperbolic numbers
Daniel Alpay, Maria Elena Luna-Elizarrarás, Michael Shapiro
We introduce the notion of a probabilistic measure which takes values in hyperbolic numbers and which satisfies the system of axioms generalizing directly Kolmogorov's system of ax…
Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis
Daniel Alpay, María Elena Luna-Elizarrarás, Michael Shapiro +1
With the goal of providing the foundations for a rigorous study of modules of bicomplex holomorphic functions, we develop a general theory of functional analysis with bicomplex sca…
Teichmüller spaces of Riemann surfaces with orbifold points of arbitrary order and cluster variables
Leonid Chekhov, Michael Shapiro
We generalize a new class of cluster type mutations for which exchange transformations are given by reciprocal polynomials. In the case of second-order polynomials of the form $x+2…
Finite difference operators with a finite--band spectrum
F. Peherstorfer, P. Yuditskii
We study the correspondence between almost periodic difference operators and algebraic curves (spectral surfaces). An especial role plays the parametrization of the spectral curves…
Finite differrence operators with a finite--band spectrum
M. Shapiro, V. Vinnikov, P. Yuditskii
We discuss a functional model for multi--diagonal selfadjoint operators with almost periodic coefficients that generalizes the well known model for finite band Jacobi matrices. It…