Let E , E∗ be Hilbert spaces. Given a Hilbert space H of holomorphic functions in a domain Ω in C, consider the multiplier space MH(E , E∗). It is shown that for “nice enough” H, the following statements are equivalent for f ∈ MH(E , E∗): (1) There exists a g ∈ MH(E∗, E) such that g(z)f(z) = IE for all z ∈ Ω. (2) There exists a Hilbert space Ec and fc ∈ MH(Ec, E∗) such that F (z) := [ f(z) fc(z...

A formula is given for the completeness radius of a random exponential system {tleiξnt}pn−1 l=0,n∈Z in terms of the probability measures of ξn. The purpose of this note is to formulate a probabilistic version of the celebrated Beurling-Malliavin theorem on the completeness radius of a sequence of complex exponentials [1]. First, to state the Beurling-Malliavin theorem, let Λ = {λn}n∈Z be a sequ...

We define tensor product decompositions of E0-semigroups with a structure analogous to a classical theorem of Beurling. Such decompositions can be characterized by adaptedness and exactness of unitary cocycles. For CCR-flows we show that such cocycles are convergent.

We extend monotone quasiconformal mappings from dimension n to n + 1 while preserving both monotonicity and quasiconformality. The extension is given explicitly by an integral operator. In the case n = 1 it yields a refinement of the Beurling-Ahlfors extension.

B. Beckman: Codebreakers: Arne Beurling and the Swedish Crypto Program during World War II, American Mathematical Society, Providence, 2002, 259 pp., $39, ISBN 0-8218-2889-4 All stories about cryptanalytical work prior and during the World War II read like a thriller. The book under review is no exception. The author, the former head of the cryptanalytical section of FRA (The Radio Agency of th...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

We conjecture that continuous complex-valued piecewise affine maps of compact support in the complex plane have a probabilistic structure: associated with certain combinations of the first partial derivatives of such functions, there are two fields of rotations, and two martingales that are martingale transforms of each other, starting from constants of equal modulus, and ending at what one obt...

In this paper, we study sparse spike deconvolution over the space of complex-valued mea-sures when the input measure is a finite sum of Dirac masses. We introduce a modified versionof the Beurling Lasso (BLasso), a semi-definite program that we refer to as the ConcomitantBeurling Lasso (CBLasso). This new procedure estimates the target measure and the un-known noise level si...

Fabry’s theorem on the singularities of power series is improved: the maximum density in the assumptions of this theorem is replaced by an interior density of Beurling–Malliavin type. MSC classes: 30B10, 30B40.

Baiocchi et al. generalized a few years ago a classical theorem of Ingham and Beurling by means of divided differences. The optimality of their assumption has been proven by the third author of this note. The purpose of this note to extend these results to vector coefficient sums.