Related papers: On the square-free representation function of a no…
We characterize semicircular distribution by the freeness of linear and quadratic forms in noncommutative random variables from a tracial $W^*$-probability space with relaxed moment conditions.
We investigate non-correlation of Fourier coefficients of Maass forms against a class of real oscillatory functions, in analogy to known results with Frobenius trace functions. We also establish an equidistribution result for twisted…
We study the behavior of representation varieties of quivers with relations under the operation of node splitting. We show how splitting a node gives a correspondence between certain closed subvarieties of representation varieties for…
The aim of this paper is to discuss some applications of the relation between Seiberg-Witten theory and two natural norms defined on the first cohomology group of a closed 3-manifold N - the Alexander and Thurston norms. We start by giving…
We discuss an alternative version of non- relativistic Newtonian mechanics in terms of a real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme correspondent with the standard formulation.…
We show that there are no non-trivial linear dependencies among p-norms of vectors in finite dimensions that hold for all p. The proof is by complex analytic continuation.
Given commutative, unital rings $A$ and $B$ with a ring homomorphism $A\to B$ making $B$ free of finite rank as an $A$-module, we can ask for a "trace" or "norm" homomorphism taking algebraic data over $B$ to algebraic data over $A$. In…
We prove symplectic non-squeezing for the cubic nonlinear Schr\"odinger equation on the line via finite-dimensional approximation.
Every quadratic form represents 0; therefore, if we take any number of quadratic forms and ask which integers are simultaneously represented by all members of the collection, we are guaranteed a nonempty set. But when is that set more than…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
We describe a standard form for the elements in the universal field of fractions of free associative algebras (over a commutative field). It is a special version of the normal form provided by Cohn and Reutenauer and enables the use of…
We give a general statement of the convolution method so that one can provide explicit asymptotic estimations for all averages of square-free supported arithmetic functions that have a sufficiently regular order on the prime numbers and…
We use Bourgain's recent bound for short exponential sums to prove certain independence results related to the distribution of squarefree numbers in arithmetic progressions.
We study the boundary free energy of the XXZ spin-$\tf{1}{2}$ chain subject to diagonal boundary fields. We first show that the representation for its finite Trotter number approximant obtained by Bortz, Frahm and G\"{o}hmann is related to…
We provide a non-renormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field…
In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of…
Free field representations of the affine superalgebra $A(1,0)^{(1)}$ at level $k$ are needed in the description of the noncritical $N=2$ string. The superalgebra admits two inequivalent choices of simple roots. We give the Wakimoto…
The formula for correlation functions based on quantum $A_\infty$ algebras in arXiv:2203.05366, arXiv:2305.11634, and arXiv:2305.13103 requires us to divide the action into the free part and the interaction part. We present a new form of…
We associate a deformation of Heisenberg algebra to the suitably normalized Yang $R$-matrix and we investigate its properties. Moreover, we construct new examples of quantum vertex algebras which possess the same representation theory as…
The foundation for the theory of correlation functions of exactly solvable models is determinant representation. Determinant representation permit to describe correlation functions by classical completely integrable differential equations…