Related papers: Fourier non-uniqueness sets from totally real numb…

Let $l\geq 6$ be any integer, where $l\equiv 2$ mod $4$. Suppose that $\mu(\tau)d\tau$ is a measure with bounded variation and is supported on a compact subset of the complex plane, where…

We give an equivalent expression for the $K$-functional associated to the pair of operator spaces $(R,C)$ formed by the rows and columns respectively. This yields a description of the real interpolation spaces for the pair $(M_n(R),…

We find new simple conditions for support of a discrete measure on Euclidean space to be a finite union of translated lattices. The arguments are based on a local analog of Wiener's Theorem on absolutely convergent trigonometric series and…

In this work, we study the Hermite interpolation on $n$-dimensional non-equally spaced, rectilinear grids over a field $\Bbbk $ of characteristic zero, given the values of the function at each point of the grid and the partial derivatives…

We study the left $K$-invariant $L^r$-Schwartz space and its Fourier transform on split rank one semisimple symmetric spaces $G/H$ for $0<r\leq 2$. We explicitly determine the kernel of the Fourier transform and show that it is spanned by…

It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular,…

We investigate the multidimensional Schrodinger operator L(q) with complex-valued periodic, with respect to a lattice, potential q when the Fourier coefficients of q with respect to the orthogonal system {exp(i(a,x))}, where a changes in…

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…

We study the Fourier transform of the absolute value of a polynomial on a finite-dimensional vector space over a local field of characteristic 0. We prove that this transform is smooth on an open dense set. We prove this result for the…

We establish sufficient conditions on discrete subsets of $\mathbb{R}^d$ for them to form a uniqueness or a non-uniqueness pair for the fractional Laplacian. Specifically, assuming that $f=0$ on $\Lambda$ and that $(-\Delta)^sf=0$ on $M$,…

The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…

This paper deals with the set of the real projections of the zeros of an arbitrary almost periodic function defined in a vertical strip $U$. It provides practical results in order to determine whether a real number belongs to the closure of…

Let $\varphi: \mathbb{P}^{n}_{F} \to \mathbb{P}^{n}_{F}$ where $F$ is a complete valued field. If $x$ is a fixed point, such that the action of $\varphi$ on $T_{x}$ has eigenvalues $\lambda_{1}, \ldots, \lambda_{n}$, with $\lambda_{1},…

The Schwartz space $\mathcal{S}(\mathbb{R}^N)$ is not invariant under the $(k,a)$-generalized Fourier transform $\mathcal{F}_{k,a}$ unless $a=2$, and in general no such adapted space is known. For $N=1$ and $\displaystyle a=\frac{2}{n}$,…

We prove the following statement about any Siegel modular form $F$ of degree $n$ and arbitrary odd level $N$ on the group $\Gamma_{0}^{(n)}(N)$. Let $A(F,T)$ denote the Fourier coefficients of $F$ and write $T=(T(i,j))$. Suppose that $F$…

We establish the existence of an infinite-dimensional fermionic symmetry in four-dimensional supersymmetric gauge theories by analyzing semiclassical photino dynamics in abelian ${\cal N}=1$ theories with charged matter. The symmetry is…

Let $P_{2k}$ be a homogeneous polynomial of degree $2k$ and assume that there exist $C>0$, $D>0$ and $\alpha \ge 0$ such that \begin{equation*} \left\langle P_{2k}f_{m},f_{m}\right\rangle_{L^2(\mathbb{S}^{d-1})}\geq \frac{1}{C\left(…

This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and…

Two measurable sets $S, \Lambda \subseteq \mathcal{R}^d$ form a Heisenberg uniqueness pair, if every bounded measure $\mu$ with support in S whose Fourier transform vanishes on {\Lambda} must be zero. We show that a quadratic hypersurface…

This paper focuses on the approximation of continuous functions on the unit sphere by spherical polynomials of degree $n$ via hyperinterpolation. Hyperinterpolation of degree $n$ is a discrete approximation of the $L^2$-orthogonal…