author={Henry Helson},
  • H. Helson
  • Published 1 February 1955
  • Mathematics
is finite. Assume that the analytic function u(r, x) can be continued across some arc of the boundary of the unit circle. Then the ak are equal, beyond some point, to the terms of a periodic sequence. A number of generalizations and related results have been published [2; 3; 4; 5; 9], of which we mention in particular that of Duffin and Schaeffer [4]; these authors replace the hypothesis that u(r, x) is analytically continuable by the weaker assumption that the function is bounded in some… 

A simple proof of the theorem of P. J. Cohen

Cohen, in [ l ] , completing a line of investigations initiated by Helson [2] and Rudin [4], proved the theorem which determines the form of idempotent measures on locally compact abelian groups. As

A Simple Proof of Gödel’s Incompleteness Theorems

LetX be a real Banach space. An important question in Banach space theory is to find conditions on a closed subspace Y ⊂ X that ensure the existence of a linear projection P : X → Y such that ‖P ‖ =

Parts of measures and integer-valued transforms

In this paper G is a compact abelian group with ordered dual T. By this we mean there is a nontrivial group homomorphism 0: T —> R where R is the additive group of real numbers. Let M(G) be the usual

The non-equivalence between the trigonometric system and the system of functions with pointwise restrictions on values in the uniform and L1 norms

  • M. Wojciechowski
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2011
Let n denote the space of trigonometric polynomials of degree n i.e. n = span(e−ikt : |k| ≤ n) ⊂ Lp() and let (Ω, dx) be any mesurable space with finite measure. In this paper we use the quantitative

Measure algebras on abelian groups

The recent developments in the general field of Fourier analysis which I wish to describe, illustrate the algebraic point of view which has established itself here as well as in most other parts of

Fourier-Stieltjes Transforms which vanish at infinity off certain sets

  • L. Pigno
  • Mathematics
    Glasgow Mathematical Journal
  • 1978
In this paper G is a nondiscrete compact abelian group with character group Г and M(G) the usual convolution algebra of Borel measures on G. We designate the following subspaces of M(G) employing the

Conservation of Singularities in Functional Equations Associated to Collatz-Type Dynamical Systems; or, Dreamcatchers for Hydra Maps

It is known that the Collatz Conjecture (and the study of similar maps, here called "Hydra maps") can be stated in terms of solution sets of functional equations; or, equivalently, the fixed points

Semi-idempotent measures on abelian groups

Let M (G) denote the set of complex valued regular Borel measures on a compact abelian group G. We assume that T, the dual group of G, is a totally ordered group. Let F(G) denote the set of all /z£


A Markov sequence is a non-zero sequence of complex numbers that satisfies a homogeneous linear difference equation with constant coefficients. The terms of such a sequence M admit of a

Asymptotic expansion of Toeplitz determinants of an indicator function with discrete rotational symmetry and powers of random unitary matrices

In this short article we propose a full large N asymptotic expansion of the probability that the m power of a random unitary matrix of size N has all its eigenvalues in a given arc-interval centered



Note on harmonic functions

The statement of the theorem is close to this result of Szegö : if a power series has coefficients assuming only finitely many distinct values, and if the analytic function so defined can be

Über Potenzreihen mit endlich vielen verschiedenen Koeffizienten

Power series with bounded coefficients, Amer

  • J. Math. vol
  • 1945