Abstract. We generalize earlier results of [2], [3], [6], [13], [14] to the case of functions of n-tuples of commuting self-adjoint operators. In particular, we prove that if a function f belongs to the Besov space B ∞,1(R ), then f is operator Lipschitz and we show that if f satisfies a Hölder condition of order α, then ‖f(A1 · · · , An)− f(B1, · · · , Bn)‖ ≤ constmax1≤j≤n ‖Aj −Bj‖ α for all n...

In order to define the discrete fractional Fourier transform, Hermite Gauss-like eigenvectors are needed and one way of extracting these eigenvectors is to employ DFT commuting matrices. Recently, Pei et al. exploited the idea of obtaining higher order DFT-commuting matrices, which was introduced by Candan previously. The upper bound of O(h) approximation to N N commuting matrix is 2kþ1rN in Ca...

In this article, we show two related results on circle diffeomorphisms. The first result is on quasi-reducibility: for a Baire-dense set of α, for any diffeomorphism f of rotation number α, it is possible to accumulate Rα with a sequence hn f h−1 n , hn being a diffeomorphism. The second result is: for a Baire-dense set of α, given two commuting diffeomorphisms f and g, such that f has α for ro...

We construct the classical r-matrix structure for the Lax formulation of BC N Ruijsenaars-Schneider systems proposed in [18]. The r-matrix structure takes a quadratic form similar to the A N Ruijsenaars-Schneider Poisson bracket behavior, although the dy-namical dependence is more complicated. Commuting Hamiltonians stemming from the BC N Ruijsenaars-Schneider Lax matrix are shown to be linear ...

The commuting variety is the pairs of n × n matrices (X, Y) such that XY = YX. We introduce the diagonal commutator scheme, { (X, Y) : XY − YX is diagonal } , which we prove to be a reduced complete intersection, one component of which is the commuting variety. (We conjecture there to be only one other component.) The diagonal commutator scheme has a flat degeneration to the scheme { (X, Y) : X...

Together with spaces of constant sectional curvature and products of a real line with a manifold of constant curvature, the socalled Egorov spaces and ε-spaces exhaust the class of n-dimensional Lorentzian manifolds admitting a group of isometries of dimension at least 1 2n(n − 1) + 1, for almost all values of n [Patrangenaru V., Geom. Dedicata 102 (2003), 25–33]. We shall prove that the curvat...

We show that for every ergodic system (X, μ,T1, . . . ,Td) with commuting transformations, the average 1 Nd+1 ∑ 0≤n1,...,nd≤N−1 ∑ 0≤n≤N−1 f1(T n 1 d ∏ j=1 T n j j x) f2(T n 2 d ∏ j=1 T n j j x) · · · fd(T n d d ∏ j=1 T n j j x). converges for μ-a.e. x ∈ X as N → ∞. If X is distal, we prove that the average 1 N N ∑ i=0 f1(T n 1 x) f2(T n 2 x) · · · fd(T n d x) converges for μ-a.e. x ∈ X as N → ∞...

let g be a group. a subset x of g is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in x. if |x| ≥ |y | for any other set of pairwise non-commuting elements y in g, then x is said to be a maximal subset of pairwise non-commuting elements. in this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

BACKGROUND Active commuting is a good opportunity to accumulate physical activity (PA) across the lifespan that potentially might influence central body fat. We aimed to examine the prospective associations of active commuting at 11, 15 and 18 years of age with central body fat at 18 years. METHODS Participants were part of a large birth cohort study in Pelotas, Brazil (n = 3,649 participants...

The commuting graph of a group G, denoted by Γ(G), is the simple undirected graph whose vertices are the non-central elements of G and two distinct vertices are adjacent if and only if they commute. Let Zm be the commutative ring of equivalence classes of integers modulo m. In this paper we investigate the connectivity and diameters of the commuting graphs of GL(n,Zm) to contribute to the conje...