We consider a generalization of isometric Hilbert space operators to the multivariable setting. We study some of the basic properties of these tuples of commuting operators and we explore several examples. In particular, we show that the d-shift, which is important in the dilation theory of d-contractions (or row contractions), is a d-isometry. As an application of our techniques we prove a the...

The author studies trends in commuting to the city of Zagreb in Croatia, Yugoslavia. Commuter surveys and bivariate analysis are used to describe the socioeconomic level, occupational status, transportation method, and place of residence of rural and urban residents who commute to the city. (SUMMARY IN ENG AND RUS)

We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions which are power of a prime is presented. It is also proved that in any dimension d ...

We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions which are power of a prime is presented. It is also proved that in any dimension d ...

Higher-rank versions of Wold decomposition are shown to hold for doubly commuting isometric representations of product systems of C∗correspondences over N 0 , generalising the classical result for a doubly commuting pair of isometries due to M. S lociński. Certain decompositions are also obtained for the general, not necessarily doubly commuting, case and several corollaries and examples are pr...

We find characterization for the distinguished varieties in symmetrized polydisc $\mathbb G_n \; (n\geq 2)$ and thus generalize work [\textit{J. Funct. Anal.}, 266 (2014), 5779 -- 5800] on G_2$ by author Shalit. show that a variety $\Lambda$ G_n$ is part of an algebraic curve, which set-theoretic complete intersection, can be represented Taylor joint spectrum $n-1$ commuting scalar matrices sat...