Related papers: Sectorial Paley-Wiener Theorem

Given a complex polynomial $P$ with zeroes $z_1,\dotsc,z_d$, we show that the asymptotic zero-counting measure of the iterated derivatives $Q^{(n)}, \ n=1,2,\dotsc$, where $Q=R/P$ is any irreducible rational function, converges to an…

We consider a reproducing kernel Hilbert space of discrete entire functions on the square lattice $\mathbb Z^2$ inspired by the classical Paley-Wiener space of entire functions of exponential growth in the complex plane. For such space we…

One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument.

In this paper, we study some typical arithmetic properties of Euler's totient function of polynomials over finite fields. Especially, we study polynomial analogues of some classical conjectures about Euler's totient function, such as…

In this paper we give a factorization theorem for the ring of exponential polynomials in many variables over an algebraically closed field of characteristic 0 with an exponentiation. This is a generalization of the factorization theorem due…

We discuss Lomonosov's proof of the Pontryagin-Krein Theorem on invariant maximal non-positive subspaces, prove the refinement of one theorem from \cite{OShT} on common fixed points for a group of fractional-linear maps of operator ball and…

In this paper, we show that the expansions of functions from $L^p$-Paley-Wiener type spaces in terms of the prolate spheroidal wave functions converge almost everywhere for $1<p<\infty$, even in the cases when they might not converge in…

Using the polynomial method of Dvir \cite{dvir}, we establish optimal estimates for Kakeya sets and Kakeya maximal functions associated to algebraic varieties $W$ over finite fields $F$. For instance, given an $n-1$-dimensional projective…

We prove an almost continuous version of Dye's theorem: any two non-atomic probability measure preserving homeomorphisms of Polish spaces are almost continuously orbit equivalent. More precisely they are orbit equivalent by a map which is…

We extend Edmonds' Branching Theorem to locally finite infinite digraphs. As examples of Oxley or Aharoni and Thomassen show, this cannot be done using ordinary arborescences, whose underlying graphs are trees. Instead we introduce the…

A mid-point theorem is proved in an elementary way for the U type shape of functions that arise out of exponential quadratic functions. These results are inspired from epidemic patterns and growth over a time period. Key words: natural…

In this paper we use the Vandermonde matrices and their properties to give a new proof of the classical result of Karl Weierstrass about the approximation of continuous functions $f$ on closed intervals, using a sequence of polynomials. The…

We consider transcendental entire functions of finite order for which the zeros and $1$-points are in disjoint sectors. Under suitable hypotheses on the sizes of these sectors we show that such functions must have a specific form, or that…

In this note we present some generalized versions of the Krein-Rutman theorem for sectorial operators. They are formulated in a fashion that can be easily applied to elliptic operators. Another feature of these generalized versions is that…

We extend Orlov's result that certain functors between derived categories of smooth projective varieties are Fourier--Mukai transforms to the case when those varieties are smooth and proper.

We study projective functions. We prove that projective functions generalise lower and upper-semianalytic ones while being stable by composition and difference. We show that the class of projective functions is closed under sums,…

Let $G$ be (the rational points of) a connected reductive group over a local non-archimedean field $F$. In this article we formulate and prove a property of an $F$-spherical homogeneous $G$-space (which in addition satisfies the finite…

The classical Szeg\H{o}-Verblunsky theorem relates integrability of the logarithm of the absolutely continuous part of a probability measure on the circle to square summability of the sequence of recurrence coefficients for the orthogonal…

We establish a version of the Beurling-Pollard theorem for operator synthesis and apply it to derive some results on linear operator equations and to prove a Beurling-Pollard type theorem for Varopoulos tensor algebras. Additionally we…

In the first part of the note we prove that a sufficient condition (due to Simons) for the convexity of the closure of the domain/range of a monotone operator is also necessary when the operator has bounded domain and is maximal. Simons'…