Related papers: Surjectivity of convolution operators on harmonic …

We consider functions $f: \mathbb{Z} \to \mathbb{R}$ and kernels $u: \{-n, \cdots, n\} \to \mathbb{R}$ normalized by $\sum_{\ell = -n}^{n} u(\ell) = 1$, making the convolution $u \ast f$ a "smoother" local average of $f$. We identify which…

In this note we study two related questions. (1) For a compact group G, what are the ranges of the convolution maps on A(GXG) given for u,v in A(G) by $u X v |-> u*v' ($v'(s)=v(s^{-1})$) and $u X v |-> u*v$? (2) For a locally compact group…

Within the framework of quantum harmonic analysis, for a locally compact group $G$ with a square-integrable, irreducible unitary representation, we analyze the eigenvalue distributions of convolutions between indicator functions on $G$ and…

The classical lemma of Borel reads: any power series with real coefficients is the Taylor series of a smooth function. Algebraically this means the surjectivity of the completion map at a point, $C^\infty(\Bbb{R}^n) \twoheadrightarrow…

Let $G$ be a compact Lie group, and let $LG$ denote the corresponding loop group. Let $(X,\omega)$ be a weakly symplectic Banach manifold. Consider a Hamiltonian action of $LG$ on $(X,\omega)$, and assume that the moment map $\mu: X \to…

Let $F$, $S$ be bounded measurable sets in $\mathbb{R}^d$. Let $P_F : L^2(\mathbb{R}^d) \rightarrow L^2(\mathbb{R}^d) $ be the orthogonal projection on the subspace of functions with compact support on $F$, and let $B_S : L^2(\mathbb{R}^d)…

The aim of this paper is to give a new proof that any very weak $s$-harmonic function $u$ in the unit ball $B$ is smooth. As a first step, we improve the local summability properties of $u$. Then, we exploit a suitable version of the…

In this paper, we prove various radius results and obtain sufficient conditions using the convolution for the Ma-Minda classes $\mathcal{S}^*(\psi)$ and $\mathcal{C}(\psi)$ of starlike and convex analytic functions. We also obtain the Bohr…

J.C.Lagarias (2000) conjectured that if $\mu$ is a complex measure on p-dimensional Euclidean space with a uniformly discrete support and its spectrum (Fourier transform) is also a measure with a uniformly discrete support, then the support…

Let $X$ be a smooth irreducible projective variety over a field $\mathbf{k}$ of dimension $d.$ Let $\tau: \mathbb{Q}_l\to \mathbb{C}$ be any field embedding. Let $f: X\to X$ be a surjective endomorphism. We show that for every…

In this paper we will study the homological properties of various natural modules associated to the Fourier algebra of a locally compact group. In particular, we will focus on the question of identifying when such modules will be projective…

Let X be a holomorphically separable irreducible reduced complex space, K a connected compact Lie group acting on X by holomorphic transformations, theta : K -> K a Weyl involution, and mu : X -> X an antiholomorphic involution map…

One of the important questions related to any integral transform on a manifold M or on a homogeneous space G/K is the description of the image of a given space of functions. If M=G/K, where (G,K) is a Gelfand pair, then the harmonic…

Consider a reductive group G over a non-archimedean local field. The Galois group Gal(C/Q) acts naturally on the category of smooth complex G-representations. We prove that this action stabilizes the class of standard modules. This…

Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no…

We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum…

We consider an operator function (F(\lambda)) for (\lambda\in(\sigma,\tau)\subseteq\mathbb R) whose values are semibounded selfadjoint operators in Hilbert space (\mathfrak H). Our main goal is to estimate the number (\mathcal…

We consider the relaxation of polyconvex functionals with linear growth with respect to the strict convergence in the space of functions of bounded variation. These functionals appears as relaxation of $F(u,\Omega):=\int_\Omega f(\nabla…

Let $(E,\mathcal E,\mu)$ be a measure space and $G\colon E\times E\to [0,\infty]$ be measurable. Moreover, let $\mathcal F\!_{ui}$ denote the set of all $q\in\mathcal E^+$ (measurable numerical functions $q\ge 0$ on $E$) such that…

We study composition operators on the Fock spaces $\mathcal{F}^2_\alpha(\mathbb{C}^n)$, problems considered include the essential norm, normality, spectra, cyclicity and membership in the Schatten classes. We give perfect answers for these…