We construct various isometry groups of Urysohn space (the unique complete separable metric space which is universal and homogeneous), including abelian groups which act transitively, and free groups which are dense in the full isometry group.

We construct various isometry groups of Urysohn space (the unique complete separable metric space that is universal and homogeneous), including abelian groups which act transitively, and free groups which are dense in the full isometry group.

In this paper we characterize weighted substitution operators between L-spaces of vector-valued functions and also make an attempt to characterize isometry and partial isometry of these operators.

We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.

A Fuchsian group is a discrete subgroup of PSL(2,R). As such it acts discontinuously on H (the upper half plane model of the hyperbolic plane) by fractional linear transformations. This action induces an action on the real line. It is well known that if an isometry of H fixes a point of the real line then the point is one of a pair, in the case that the isometry is hyperbolic or the isometry in...

Leveraging recent advances in additive combinatorics, we exhibit explicit matrices satisfying the Restricted Isometry Property with better parameters. Namely, for $$\varepsilon=3.26\cdot 10^{-7}$$ , large $$k$$ and $$k^{2-\varepsilon} \le N\le k^{2+\varepsilon}$$ construct $$n \times N$$ RIP of order $$k = \Omega( n^{1/2+\varepsilon/4)}$$ .

Let $$\{a_n\}_{n\ge 0}$$ and $$\{b_n\}_{n\ge be sequences of scalars. Suppose $$a_n \ne 0$$ for all $$n \ge . We consider the tridiagonal kernel (also known as band with bandwidth one) $$\begin{aligned} k(z, w) = \sum _{n=0}^\infty ((a_n + b_n z)z^n) \overline{(({a}_n {b}_n {w}) {w}^n)} \qquad (z, w \in \mathbb {D}), \end{aligned}$$ where $$\mathbb {D} \{z {C}: |z| < 1\}$$ Denote by $$M_z$$ mul...