Related papers: Multi-dimensional $\rho$-almost periodic type func…

We define a class of $Y(sl_{(m|n)})$ Yangian invariant Haldane-Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials. Using some properties of…

We consider one-dimensional Schr\"odinger operators with generalized almost periodic potentials with jump discontinuities and $\delta$-interactions. For operators of this kind we introduce a rotation number in the spirit of Johnson and…

We propose an ansatz for the wave function of a non-interacting quantum particle in a deterministic quasicrystalline potential. It is applicable to both continuous and discrete models and includes Sutherland's hierarchical wave function as…

In this paper, we first propose a concept of weighted pseudo-almost periodic functions on time scales and study some basic properties of weighted pseudo-almost periodic functions on time scales. Then, we establish some results about the…

In this paper we consider Wannier functions of quasi-periodic g-gap ($g\geq 1$) potentials and investigate their main properties. In particular, we discuss the problem of averaging underlying the definition of Wannier functions for both…

We generalize techniques of Addison to a vastly larger context. We obtain integral representations in terms of the first periodic Bernoulli polynomial for a number of important special functions including the Lerch zeta, polylogarithm,…

In this chapter, we describe three related studies of the universal physics of two-component unitary Fermi gases with resonant short-ranged interactions. First we discuss an ab initio auxiliary field quantum Monte Carlo technique for…

This paper shows that for a given irreducible representation $\rho$ of $\Gamma/\Gamma_1$, the two functions dim($M_k(\Gamma_1,\rho)$) and dim($S_k(\Gamma_1,\rho)$) of $k$ are almost linear functions.

In important work on the parity of the partition function, Ono related values of the partition function to coefficients of a certain mock theta function modulo 2. In this paper, we use M\"obius inversion to give analogous results which…

We construct $\Delta$-operators $F[\Delta]$ on the space of almost symmetric functions $\mathscr{P}_{as}^{+}$. These operators extend the usual $\Delta$-operators on the space of symmetric functions $\Lambda \subset \mathscr{P}_{as}^{+}$…

Let us consider the Schr\"{o}dinger operator $\mathcal{L}=-\Delta+V$ on $\mathbb R^d$ with $d\geq3$, where $\Delta$ is the Laplacian operator on $\mathbb R^d$ and the nonnegative potential $V$ belongs to certain reverse H\"{o}lder class…

In this paper we continue the study of important Banach spaces of slice hyperholomorphic functions on the quaternionic unit ball by investigating the BMO- and VMO-spaces of slice hyperholomorphic functions. We discuss in particular…

The aim of this paper is to study the problem of existence of remotely almost periodic solutions for the scalar differential equation $x'=f(t,x),$ where $f:\mathbb R\times \mathbb R\to \mathbb R$ is a continuous, monotone in $x$ and…

It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in…

By methods of harmonic analysis, we identify large classes of Banach spaces invariant of periodic Fourier multipliers with symbols satisfying the classical Marcinkiewicz type conditions. Such classes include general (vector-valued) Banach…

In this paper we study the asymptotic behaviour via Gamma-convergence of some integral functionals which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals are defined in…

H.Bohr in 1930 proved that if a holomorphic bounded function on a strip is almost periodic on a straight line in the strip, then it is almost periodic on the whole strip. We find some conditions when the result is valid for holomorphic…

The oscillations described by periodic functions play an important role in many areas. In the present paper, we study periodic functions which belong to the class of the $n$-member chains. The self-intersection and local singular points of…

We study a new class of functions that arise naturally in quaternionic analysis, we call them "quasi regular functions". Like the well-known quaternionic regular functions, these functions provide representations of the quaternionic…

In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…