Related papers: On the semi-regular frames of translates

We describe $\frac{1}{2}$-derivations, and hence transposed Poisson algebra structures, on Witt type Lie algebras $V(f)$, where $f:\Gamma\to\mathbb C$ is non-trivial and $f(0)=0$. More precisely, if $|f(\Gamma)|\ge 4$, then all the…

Let $G$ be a connected, simply connected, nilpotent Lie group whose irreducible unitary representations are square-integrable modulo the center. We obtain characterization results for reproducing formulas associated with the left…

The partial transpose of density matrices in many-body quantum systems, in which one takes the transpose only for a subsystem of the full Hilbert space, has been recognized as a useful tool to diagnose quantum entanglement. It can be used,…

Let $A$ be a subset of positive relative upper density of $\PP^d$, the $d$-tuples of primes. We prove that $A$ contains an affine copy of any finite set $F\subs\Z^d$, which provides a natural multi-dimensional extension of the theorem of…

A classification of the semisimple subalgebras of the Lie algebra of traceless $3\times 3$ matrices with complex entries, denoted $A_2$, is well-known. We classify its nonsemisimple subalgebras, thus completing the classification of the…

In this paper we study algorithms for tiling problems. We show that the conditions $(T1)$ and $(T2)$ of Coven and Meyerowitz, conjectured to be necessary and sufficient for a finite set $A$ to tile the integers, can be checked in time…

We present in this report 1+1 dimensional nonlinear partial differential equation integrable through inverse scattering transform. The integrable system under consideration is a pseudo-Hermitian reduction of a matrix generalization of…

In this paper we prove an explicit matching theorem for some Hecke elements in the case of (possibly ramified) cyclic base change for general linear groups over local fields of characteristic zero with odd residue characteristic under a…

It is known that if $\Omega \subset \mathbb{R}^{d}$ belongs to a class of multi-tiling domains when translated by a lattice $\Lambda$, there exists a Riesz basis of exponentials for $L^{2}(\Omega)$ constructed using $k$ translates of the…

For delta operator $aD-bD^{p+1}$ we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case $D-\frac{1}{2}D^2$ we show that the corresponding Bessel-Carlitz polynomials are moments of the…

A variety of techniques have been developed for the approximation of non-periodic functions. In particular, there are approximation techniques based on rank-$1$ lattices and transformed rank-$1$ lattices, including methods that use sampling…

In 1949, Denis Gabor introduced the ``complex signal'' (nowadays called ``analytic signal'') by combining a real function $f$ with its Hilbert transform $Hf$ to a complex function $f+ iHf$. His aim was to extract phase information, an idea…

A birational transformation f: P^n --> Z, where Z is a nonsingular variety of Picard number 1, is called a special birational transformation of type (a, b) if f is given by a linear system of degree a, its inverse is given by a linear…

In this paper, we show how to construct an orthonormal basis from Riesz basis by assuming that the fractional translates of a single function in the core subspace of the fractional multiresolution analysis form a Riesz basis instead of an…

We say that a function $f \in L^1(\mathbb{R})$ tiles at level $w$ by a discrete translation set $\Lambda \subset \mathbb{R}$, if we have $\sum_{\lambda \in \Lambda} f(x-\lambda)=w$ a.e. In this paper we survey the main results, and prove…

Let $G$ be the $ax+b$ group. There are essentially two irreducible infinite dimensional unitary representations of $G$, $(\mu, L^2(\mathbb R^+))$ and $(\mu^*, L^2(\mathbb R^+))$. In this paper, we give various characterizations about smooth…

In this paper, we propose new regularization, where integer-order differential operators are replaced by fractional-order operators. Regularization for quantum field theories based on application of the Riesz fractional derivatives of…

We are concerned with $T$-periodic solutions of nonautonomous parabolic problem of the form $u_t = \Delta u + V(x) u + f(t,x,u)$, $t >0$, $x \in \mathbb{R}^N$, with $V \in L^\infty (\mathbb{R}^N)+L^p(\mathbb{R}^N)$, $p \geq N$ and…

We consider square matrices A that commute with a fixed square matrix K, both with entries in a field F not of characteristic 2. When K^2=I, Tao and Yasuda defined A to be generalized centrosymmetric with respect to K. When K^2=-I, we…

A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down…