Related papers: Orthonormal bases generated by Cuntz algebras

By using C*-correspondences and Cuntz-Pimsner algebras, we associate to every subshift (also called a shift space) $X$ a C*-algebra $O_X$, which is a generalization of the Cuntz-Krieger algebras. We show that $O_X$ is the universal…

We construct bar-invariant $\mathbb{Z}[q^{\pm 1/2}]-$bases of the quantum cluster algebra of the Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the cluster algebra of…

The $q$-Onsager algebra $O_q$ has a presentation involving two generators $W_0$, $W_1$ and two relations, called the $q$-Dolan/Grady relations. The alternating central extension $\mathcal O_q$ has a presentation involving the alternating…

In this paper, we study the harmonic analysis of Bernoulli measures. We show a variety of orthonormal Fourier bases for the L^2 Hilbert spaces corresponding to certain Bernoulli measures, making use of contractive transfer operators. For…

Theorems and explicit examples are used to show how transformations between self-similar sets (general sense) may be continuous almost everywhere with respect to stationary measures on the sets and may be used to carry well known flows and…

We construct explicit exponential bases on finite unions of disjoint rectangles of $\mathbb{R}^d$ with rational vertices.

A weight basis for each finite-dimensional irreducible representation of the orthogonal Lie algebra o(2n) is constructed. The basis vectors are parametrized by the D-type Gelfand--Tsetlin patterns. Explicit formulas for the matrix elements…

A collection of subroutines and examples of their uses, as well as the underlying numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object of these routines is to produce the…

A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension 2N, known as complex quadrics. These…

Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle ($L^2(\mathcal C)$) and in $l_2(\mathbb Z)$, which are related to each other by means of the Fourier transform and the…

We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection…

For a field $F$ and an integer $d\geq 1$, we consider the universal associative $F$-algebra $A$ generated by two sets of $d+1$ mutually orthogonal idempotents. We display four bases for the $F$-vector space $A$ that we find attractive. We…

We apply recent constructions of free Baxter algebras to the study of the umbral calculus. We give a characterization of the umbral calculus in terms of Baxter algebra. This characterization leads to a natural generalization of the umbral…

Representation theory provides a suitable framework to count and classify invariants in tensor models. We show that there are two natural ways of counting invariants, one for arbitrary rank of the gauge group and a second, which is only…

We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal polynomials on the surface of quadratic surfaces of revolution,…

We show that the core inclusion arising from a Cuntz-Pimsner algebra generated by a full, faithful and dualizable correspondence is C*-discrete, and express it as a crossed-product by an action of a unitary tensor category. In particular,…

In this paper, a method for constructing a near optimal normal basis for algebraic extensions of a finite field is described. In each extension, except for the squares of basis elements, the product of two distinct normal basis elements can…

It's well know that Radial Basis Function approximants suffers of bad conditioning if the simple basis of translates is used. A recent work of M.Pazouki and R.Schaback gives a quite general way to build stable, orthonormal bases for the…

It is proved that for a vector space W, any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of [DL2] with W as a natural module. This result generalizes a result…

We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials